diff --git a/karabo_devices/shared_mem_processor/src/onlinemid_karabo/processor.py b/karabo_devices/shared_mem_processor/src/onlinemid_karabo/processor.py
index d3111f7e768cfcdd255a45e85ce9b8ad91d75c51..2ae9c658e353bcdd766363c2c300bf2c5bffb45e 100644
--- a/karabo_devices/shared_mem_processor/src/onlinemid_karabo/processor.py
+++ b/karabo_devices/shared_mem_processor/src/onlinemid_karabo/processor.py
@@ -41,8 +41,7 @@ from onlinemid.utils.karabo import Periodic_Output
 from onlinemid.dataplotters.agipd_module import AgipdModulePlotter
 from onlinemid.dataplotters.gain_stage import GainStagePlotter
 from onlinemid.utils.image_plotting import OnlinePlotHandler
-from onlinemid.roi.roi import make_onlineroi_from_roi_array
-
+from onlinemid.runningstats.call_runningstats import Runningstats
 from onlinexpcsutils import onlinexpcsutils
 import runningstats
     
@@ -156,8 +155,23 @@ class OnlineMIDProcessor(TrainMatcher.TrainMatcher):
         self.periodic_output = Periodic_Output() # default time at 300 sec
 
         self.onlineImagePlotter = OnlinePlotHandler()
+        self.onlineStats = Runningstats()
+        
+
+        self.test_roi = {
+            'Q1M1' : np.random.randint(2, size=5*512*128).reshape(5, 512, 128),
+            'Q1M2' : np.random.randint(2, size=5*512*128).reshape(5, 512, 128),
+            'Q1M3' : np.random.randint(2, size=5*512*128).reshape(5, 512, 128),
+            'Q1M4' : np.random.randint(2, size=5*512*128).reshape(5, 512, 128),
+        }
+            
+
+        
+        self.onlineStats.update_roi([('Q1M1', self.test_roi['Q1M1'])])
+        self.onlineStats.update_roi([('Q1M2', self.test_roi['Q1M2'])])
+        self.onlineStats.update_roi([('Q1M3', self.test_roi['Q1M3'])])
+        self.onlineStats.update_roi([('Q1M4', self.test_roi['Q1M4'])])
 
-        self.schemupdate_test = False
 
         # expose the get xpcs settings function
         self.KARABO_SLOT(self.get_OnlineMIDSettings)
@@ -165,13 +179,9 @@ class OnlineMIDProcessor(TrainMatcher.TrainMatcher):
         self.registerSlot(self.triggerSampleOutput)
 
         ### XPCS specific variables
-        self.online_processing_memory = None
-        self.xpcs_processing_plot = None
         self.xpcs_settings = None
 
-        # running stats specific variables
-        self.runningstats_processing_memory = None
-       
+        
         self.timeSinceLastDataPrintUpdate = 0
 
     def initialization(self):
@@ -387,54 +397,13 @@ class OnlineMIDProcessor(TrainMatcher.TrainMatcher):
         #print("asking to plot")
         #current_img = self.onlineImagePlotter.plot(train_id, detector_data_list[0][1][0])
 
-        roi_matrix = np.zeros(shape=(3,10))
-        roi_matrix[0,0] = False
-        roi_matrix[0,1] = False
-        roi_matrix[0,2] = True
-        roi_matrix[0,3] = True
-        roi_matrix[0,4] = True
-        roi_matrix[0,5] = False
-        roi_matrix[0,6] = False
-        roi_matrix[0,7] = True
-        roi_matrix[0,8] = True
-        roi_matrix[0,9] = False
-        roi_matrix[1,0] = False
-        roi_matrix[1,1] = True
-        roi_matrix[1,2] = True
-        roi_matrix[1,3] = True
-        roi_matrix[1,4] = True
-        roi_matrix[1,5] = True
-        roi_matrix[1,6] = True
-        roi_matrix[1,7] = True
-        roi_matrix[1,8] = True
-        roi_matrix[1,9] = False
-        roi_matrix[2,0] = True
-        roi_matrix[2,1] = True
-        roi_matrix[2,2] = False
-        roi_matrix[2,3] = False
-        roi_matrix[2,4] = False
-        roi_matrix[2,5] = False
-        roi_matrix[2,6] = False
-        roi_matrix[2,7] = False
-        roi_matrix[2,8] = False
-        roi_matrix[2,9] = True
-        
-        
-
-        compressed = make_onlineroi_from_roi_array(roi_matrix)
-        print(compressed)
-
-
-        #self.runningstats_processing_memory, runningstats_output_dict = runningstats.process_detector_data_list(
-        #    detector_data_list,
-        #    roi,
-        #    processing_memory = self.runningstats_processing_memory,
-        #    lit_frames = self.xpcs_settings["litFramesList"]
-        #    )
         
+        lit_frames = None
+        result = self.onlineStats.process_detector_data_list(detector_data_list, lit_frames)
+        
+        print(result)        
 
 
-        
         plot_hash = Hash()
 
         plot_hash = self.onlineImagePlotter.save(hash=plot_hash, key='first_bunch', plotter_args=(train_id, detector_data_list[0][1][0]))
diff --git a/python_package/setup.py b/python_package/setup.py
index 32d677335e7d24fb9f82a9080c6f233bdbff044f..455eaf98f94cfaa6eaf0ce6d4a3acca3b8c69d4f 100644
--- a/python_package/setup.py
+++ b/python_package/setup.py
@@ -5,7 +5,7 @@ import numpy
 from setuptools import setup, find_packages, Extension
 
 extensions = [
-    Extension('onlinemid.onlinemid.runningstats', ['src/onlinemid/runningstats.pyx', 'src/onlinemid/runningstats/runningstats_impl.cpp'],
+    Extension('onlinemid.onlinemid.runningstats', ['src/onlinemid/runningstats/runningstats.pyx', 'src/onlinemid/runningstats/runningstats_impl.cpp'],
               include_dirs=['src/onlinemid/runningstats',numpy.get_include()], 
               language='c++',
               extra_compile_args=[
diff --git a/python_package/src/onlinemid/runningstats/runningstats.py b/python_package/src/onlinemid/runningstats/call_runningstats.py
similarity index 65%
rename from python_package/src/onlinemid/runningstats/runningstats.py
rename to python_package/src/onlinemid/runningstats/call_runningstats.py
index 2a615c67aaf17e65f73be78fa5e1330ffaae8dd8..baecc93319ecdc0f9f69cec95593548358c583d9 100644
--- a/python_package/src/onlinemid/runningstats/runningstats.py
+++ b/python_package/src/onlinemid/runningstats/call_runningstats.py
@@ -3,11 +3,62 @@
 import numpy as np
 import time
 
-from .runningstats import call_roi_stats
+from .call_runningstats import call_roi_stats
 
+from onlinemid.roi.roi import make_onlineroi_from_roi_array
+class Runningstats():
+    '''
+    usecase:
 
-class runningstats():
+    from onlinemid.runningstats.call_runningstats import Runningstats
 
+
+    stats = Runningstats()
+    ...
+
+    roi_for_this_module = # np array of shape (num_rois, slowscan, fastscan)
+                          # should be true or false only
+                          # e.g. of shape (5, 512, 128)
+                          # for 5 rois that may very wel be overlapping.
+
+    this_module_name = 'Q1M1' # e.g. panel name of AGIPD
+
+    stats.update_roi([(this_module_name, roi_for_this_module)])
+
+
+    for tid, data in module_data:
+        
+        detector_data_list = [('this_module_name', module_data )]
+        lit_frames = None
+        or, e.g., 
+        lit_frames = np.array([1, 11, 21, 31])
+
+        result = stats.process_detector_data_list(detector_data_list, lit_frames)
+        # result is a list with dictionaries, that each have these entries:
+        #   "module_name" of type string, e.g.,
+        #       'Q1M1'
+        #   "bunch_resolved_roi_stats" of type np array,
+        #    if lit_frames = None, then of shape 
+        #                      numBunches x numRois x          3 
+        #     which contain    numBunches x numRois x (count, mean, std)
+        #    otherwise
+        #                      numLitFrames x numRois x          3 
+        #     which contain    numLitFrames x numRois x (count, mean, std)
+        #   "pixel_stats" are the statistics of each pixel in this data (across memory cells)
+        #    is a np array of shape
+        #          slowscan x fastscan x 3
+        #   which contains    slowscan dim x fastscan dim x (count, mean std)
+        #   "processing_time", time_to_process,
+        #                the time in seconds to process the data
+
+    Note that you can call the update roi for a given module name can be done for several unique names
+    also with different data sizes.
+    
+                
+
+
+    
+    '''
     def __init__(self, verbose=False):
         
         self.verbose = verbose
@@ -15,12 +66,13 @@ class runningstats():
         self.dtype = np.float32
 
 
-    def update_roi(self, list_of_module_name_and_online_roi_pairs):
-        for pair in list_of_module_name_and_online_roi_pairs:
+    def update_roi(self, list_of_module_name_and_roi_pairs):
+        for pair in list_of_module_name_and_roi_pairs:
             module_name = pair[0]
 
             self.ensure_init_module(module_name)
-            online_roi = pair[1]
+            
+            online_roi = make_onlineroi_from_roi_array(pair[1])
 
             self.module[module_name].update(online_roi)
 
@@ -31,7 +83,7 @@ class runningstats():
 
         # returns a list of dicts with entries
         # "module_name"
-        # "bunch_resolved_roi__stats"
+        # "bunch_resolved_roi_stats"
         # "pixel_stats"
         # "processing_time"
     ):
@@ -67,7 +119,7 @@ class runningstats():
                 print(f"Error: in process_detector_data_list in runningstats for module {module_name}: roi has image size size {self.module[module_name]['roi_datasize']} and provided module data has size {image_size}! they are not equal, aborting")
                 continue
             
-            bunch_resolved_roi__stats, pixel_stats, time_to_process = self.process(
+            bunch_resolved_roi_stats, pixel_stats, time_to_process = self.process(
                 module_data,
                 num_images,
                 image_size, 
@@ -76,21 +128,21 @@ class runningstats():
             
             result.append({
                 "module_name", module_name, 
-                "bunch_resolved_roi__stats", bunch_resolved_roi__stats,
-                "pixel_stats", pixel_stats,
+                "bunch_resolved_roi_stats", bunch_resolved_roi_stats,
+                "pixel_stats", pixel_stats.reshape(module_data.shape[1], module_data.shape[2], 3),
                 "processing_time", time_to_process,
                 })
         
         return result
             
-    
+    # private
     def ensure_init_module(self, module_name):
         if module_name not in self.module:
             if self.verbose == True:
                 print(f"runningstats: initialized module {module_name}")
             self.module[module_name] = dict()
         
-
+    # private
     def process(self,
             module_data, 
             num_images,
diff --git a/python_package/src/onlinemid/runningstats/runningstats.cpp b/python_package/src/onlinemid/runningstats/runningstats.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..6847d0712fe50f2ec0082c47685cad9203f1f762
--- /dev/null
+++ b/python_package/src/onlinemid/runningstats/runningstats.cpp
@@ -0,0 +1,12892 @@
+/* Generated by Cython 3.0.11 */
+
+/* BEGIN: Cython Metadata
+{
+    "distutils": {
+        "depends": [
+            "/home/jakobsem/.local/lib/python3.10/site-packages/numpy/_core/include/numpy/arrayobject.h",
+            "/home/jakobsem/.local/lib/python3.10/site-packages/numpy/_core/include/numpy/arrayscalars.h",
+            "/home/jakobsem/.local/lib/python3.10/site-packages/numpy/_core/include/numpy/ndarrayobject.h",
+            "/home/jakobsem/.local/lib/python3.10/site-packages/numpy/_core/include/numpy/ndarraytypes.h",
+            "/home/jakobsem/.local/lib/python3.10/site-packages/numpy/_core/include/numpy/ufuncobject.h",
+            "src/onlinemid/runningstats/runningstats_impl.h"
+        ],
+        "extra_compile_args": [
+            "-std=c++20",
+            "-O3",
+            "-finline-functions",
+            "-m64",
+            "-funroll-loops",
+            "-march=native"
+        ],
+        "include_dirs": [
+            "src/onlinemid/runningstats",
+            "/home/jakobsem/.local/lib/python3.10/site-packages/numpy/_core/include"
+        ],
+        "language": "c++",
+        "name": "onlinemid.onlinemid.runningstats",
+        "sources": [
+            "src/onlinemid/runningstats/runningstats.pyx",
+            "src/onlinemid/runningstats/runningstats_impl.cpp"
+        ]
+    },
+    "module_name": "onlinemid.onlinemid.runningstats"
+}
+END: Cython Metadata */
+
+#ifndef PY_SSIZE_T_CLEAN
+#define PY_SSIZE_T_CLEAN
+#endif /* PY_SSIZE_T_CLEAN */
+#if defined(CYTHON_LIMITED_API) && 0
+  #ifndef Py_LIMITED_API
+    #if CYTHON_LIMITED_API+0 > 0x03030000
+      #define Py_LIMITED_API CYTHON_LIMITED_API
+    #else
+      #define Py_LIMITED_API 0x03030000
+    #endif
+  #endif
+#endif
+
+#include "Python.h"
+#ifndef Py_PYTHON_H
+    #error Python headers needed to compile C extensions, please install development version of Python.
+#elif PY_VERSION_HEX < 0x02070000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
+    #error Cython requires Python 2.7+ or Python 3.3+.
+#else
+#if defined(CYTHON_LIMITED_API) && CYTHON_LIMITED_API
+#define __PYX_EXTRA_ABI_MODULE_NAME "limited"
+#else
+#define __PYX_EXTRA_ABI_MODULE_NAME ""
+#endif
+#define CYTHON_ABI "3_0_11" __PYX_EXTRA_ABI_MODULE_NAME
+#define __PYX_ABI_MODULE_NAME "_cython_" CYTHON_ABI
+#define __PYX_TYPE_MODULE_PREFIX __PYX_ABI_MODULE_NAME "."
+#define CYTHON_HEX_VERSION 0x03000BF0
+#define CYTHON_FUTURE_DIVISION 1
+#include <stddef.h>
+#ifndef offsetof
+  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
+#endif
+#if !defined(_WIN32) && !defined(WIN32) && !defined(MS_WINDOWS)
+  #ifndef __stdcall
+    #define __stdcall
+  #endif
+  #ifndef __cdecl
+    #define __cdecl
+  #endif
+  #ifndef __fastcall
+    #define __fastcall
+  #endif
+#endif
+#ifndef DL_IMPORT
+  #define DL_IMPORT(t) t
+#endif
+#ifndef DL_EXPORT
+  #define DL_EXPORT(t) t
+#endif
+#define __PYX_COMMA ,
+#ifndef HAVE_LONG_LONG
+  #define HAVE_LONG_LONG
+#endif
+#ifndef PY_LONG_LONG
+  #define PY_LONG_LONG LONG_LONG
+#endif
+#ifndef Py_HUGE_VAL
+  #define Py_HUGE_VAL HUGE_VAL
+#endif
+#define __PYX_LIMITED_VERSION_HEX PY_VERSION_HEX
+#if defined(GRAALVM_PYTHON)
+  /* For very preliminary testing purposes. Most variables are set the same as PyPy.
+     The existence of this section does not imply that anything works or is even tested */
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #define CYTHON_COMPILING_IN_LIMITED_API 0
+  #define CYTHON_COMPILING_IN_GRAAL 1
+  #define CYTHON_COMPILING_IN_NOGIL 0
+  #undef CYTHON_USE_TYPE_SLOTS
+  #define CYTHON_USE_TYPE_SLOTS 0
+  #undef CYTHON_USE_TYPE_SPECS
+  #define CYTHON_USE_TYPE_SPECS 0
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #if PY_VERSION_HEX < 0x03050000
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_INTERNALS
+  #define CYTHON_USE_UNICODE_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #undef CYTHON_AVOID_BORROWED_REFS
+  #define CYTHON_AVOID_BORROWED_REFS 1
+  #undef CYTHON_ASSUME_SAFE_MACROS
+  #define CYTHON_ASSUME_SAFE_MACROS 0
+  #undef CYTHON_UNPACK_METHODS
+  #define CYTHON_UNPACK_METHODS 0
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_GIL
+  #define CYTHON_FAST_GIL 0
+  #undef CYTHON_METH_FASTCALL
+  #define CYTHON_METH_FASTCALL 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #ifndef CYTHON_PEP487_INIT_SUBCLASS
+    #define CYTHON_PEP487_INIT_SUBCLASS (PY_MAJOR_VERSION >= 3)
+  #endif
+  #undef CYTHON_PEP489_MULTI_PHASE_INIT
+  #define CYTHON_PEP489_MULTI_PHASE_INIT 1
+  #undef CYTHON_USE_MODULE_STATE
+  #define CYTHON_USE_MODULE_STATE 0
+  #undef CYTHON_USE_TP_FINALIZE
+  #define CYTHON_USE_TP_FINALIZE 0
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+  #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC
+    #define CYTHON_UPDATE_DESCRIPTOR_DOC 0
+  #endif
+  #undef CYTHON_USE_FREELISTS
+  #define CYTHON_USE_FREELISTS 0
+#elif defined(PYPY_VERSION)
+  #define CYTHON_COMPILING_IN_PYPY 1
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #define CYTHON_COMPILING_IN_LIMITED_API 0
+  #define CYTHON_COMPILING_IN_GRAAL 0
+  #define CYTHON_COMPILING_IN_NOGIL 0
+  #undef CYTHON_USE_TYPE_SLOTS
+  #define CYTHON_USE_TYPE_SLOTS 0
+  #ifndef CYTHON_USE_TYPE_SPECS
+    #define CYTHON_USE_TYPE_SPECS 0
+  #endif
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #if PY_VERSION_HEX < 0x03050000
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_INTERNALS
+  #define CYTHON_USE_UNICODE_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #undef CYTHON_AVOID_BORROWED_REFS
+  #define CYTHON_AVOID_BORROWED_REFS 1
+  #undef CYTHON_ASSUME_SAFE_MACROS
+  #define CYTHON_ASSUME_SAFE_MACROS 0
+  #undef CYTHON_UNPACK_METHODS
+  #define CYTHON_UNPACK_METHODS 0
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_GIL
+  #define CYTHON_FAST_GIL 0
+  #undef CYTHON_METH_FASTCALL
+  #define CYTHON_METH_FASTCALL 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #ifndef CYTHON_PEP487_INIT_SUBCLASS
+    #define CYTHON_PEP487_INIT_SUBCLASS (PY_MAJOR_VERSION >= 3)
+  #endif
+  #if PY_VERSION_HEX < 0x03090000
+    #undef CYTHON_PEP489_MULTI_PHASE_INIT
+    #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #elif !defined(CYTHON_PEP489_MULTI_PHASE_INIT)
+    #define CYTHON_PEP489_MULTI_PHASE_INIT 1
+  #endif
+  #undef CYTHON_USE_MODULE_STATE
+  #define CYTHON_USE_MODULE_STATE 0
+  #undef CYTHON_USE_TP_FINALIZE
+  #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1 && PYPY_VERSION_NUM >= 0x07030C00)
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+  #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC
+    #define CYTHON_UPDATE_DESCRIPTOR_DOC 0
+  #endif
+  #undef CYTHON_USE_FREELISTS
+  #define CYTHON_USE_FREELISTS 0
+#elif defined(CYTHON_LIMITED_API)
+  #ifdef Py_LIMITED_API
+    #undef __PYX_LIMITED_VERSION_HEX
+    #define __PYX_LIMITED_VERSION_HEX Py_LIMITED_API
+  #endif
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #define CYTHON_COMPILING_IN_LIMITED_API 1
+  #define CYTHON_COMPILING_IN_GRAAL 0
+  #define CYTHON_COMPILING_IN_NOGIL 0
+  #undef CYTHON_CLINE_IN_TRACEBACK
+  #define CYTHON_CLINE_IN_TRACEBACK 0
+  #undef CYTHON_USE_TYPE_SLOTS
+  #define CYTHON_USE_TYPE_SLOTS 0
+  #undef CYTHON_USE_TYPE_SPECS
+  #define CYTHON_USE_TYPE_SPECS 1
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #undef CYTHON_USE_ASYNC_SLOTS
+  #define CYTHON_USE_ASYNC_SLOTS 0
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #undef CYTHON_USE_UNICODE_INTERNALS
+  #define CYTHON_USE_UNICODE_INTERNALS 0
+  #ifndef CYTHON_USE_UNICODE_WRITER
+    #define CYTHON_USE_UNICODE_WRITER 0
+  #endif
+  #undef CYTHON_USE_PYLONG_INTERNALS
+  #define CYTHON_USE_PYLONG_INTERNALS 0
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #undef CYTHON_ASSUME_SAFE_MACROS
+  #define CYTHON_ASSUME_SAFE_MACROS 0
+  #undef CYTHON_UNPACK_METHODS
+  #define CYTHON_UNPACK_METHODS 0
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_GIL
+  #define CYTHON_FAST_GIL 0
+  #undef CYTHON_METH_FASTCALL
+  #define CYTHON_METH_FASTCALL 0
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #ifndef CYTHON_PEP487_INIT_SUBCLASS
+    #define CYTHON_PEP487_INIT_SUBCLASS 1
+  #endif
+  #undef CYTHON_PEP489_MULTI_PHASE_INIT
+  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #undef CYTHON_USE_MODULE_STATE
+  #define CYTHON_USE_MODULE_STATE 1
+  #ifndef CYTHON_USE_TP_FINALIZE
+    #define CYTHON_USE_TP_FINALIZE 0
+  #endif
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+  #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC
+    #define CYTHON_UPDATE_DESCRIPTOR_DOC 0
+  #endif
+  #undef CYTHON_USE_FREELISTS
+  #define CYTHON_USE_FREELISTS 0
+#elif defined(Py_GIL_DISABLED) || defined(Py_NOGIL)
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_CPYTHON 0
+  #define CYTHON_COMPILING_IN_LIMITED_API 0
+  #define CYTHON_COMPILING_IN_GRAAL 0
+  #define CYTHON_COMPILING_IN_NOGIL 1
+  #ifndef CYTHON_USE_TYPE_SLOTS
+    #define CYTHON_USE_TYPE_SLOTS 1
+  #endif
+  #ifndef CYTHON_USE_TYPE_SPECS
+    #define CYTHON_USE_TYPE_SPECS 0
+  #endif
+  #undef CYTHON_USE_PYTYPE_LOOKUP
+  #define CYTHON_USE_PYTYPE_LOOKUP 0
+  #ifndef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #ifndef CYTHON_USE_PYLONG_INTERNALS
+    #define CYTHON_USE_PYLONG_INTERNALS 0
+  #endif
+  #undef CYTHON_USE_PYLIST_INTERNALS
+  #define CYTHON_USE_PYLIST_INTERNALS 0
+  #ifndef CYTHON_USE_UNICODE_INTERNALS
+    #define CYTHON_USE_UNICODE_INTERNALS 1
+  #endif
+  #undef CYTHON_USE_UNICODE_WRITER
+  #define CYTHON_USE_UNICODE_WRITER 0
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #ifndef CYTHON_ASSUME_SAFE_MACROS
+    #define CYTHON_ASSUME_SAFE_MACROS 1
+  #endif
+  #ifndef CYTHON_UNPACK_METHODS
+    #define CYTHON_UNPACK_METHODS 1
+  #endif
+  #undef CYTHON_FAST_THREAD_STATE
+  #define CYTHON_FAST_THREAD_STATE 0
+  #undef CYTHON_FAST_GIL
+  #define CYTHON_FAST_GIL 0
+  #ifndef CYTHON_METH_FASTCALL
+    #define CYTHON_METH_FASTCALL 1
+  #endif
+  #undef CYTHON_FAST_PYCALL
+  #define CYTHON_FAST_PYCALL 0
+  #ifndef CYTHON_PEP487_INIT_SUBCLASS
+    #define CYTHON_PEP487_INIT_SUBCLASS 1
+  #endif
+  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
+    #define CYTHON_PEP489_MULTI_PHASE_INIT 1
+  #endif
+  #ifndef CYTHON_USE_MODULE_STATE
+    #define CYTHON_USE_MODULE_STATE 0
+  #endif
+  #ifndef CYTHON_USE_TP_FINALIZE
+    #define CYTHON_USE_TP_FINALIZE 1
+  #endif
+  #undef CYTHON_USE_DICT_VERSIONS
+  #define CYTHON_USE_DICT_VERSIONS 0
+  #undef CYTHON_USE_EXC_INFO_STACK
+  #define CYTHON_USE_EXC_INFO_STACK 0
+  #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC
+    #define CYTHON_UPDATE_DESCRIPTOR_DOC 1
+  #endif
+  #ifndef CYTHON_USE_FREELISTS
+    #define CYTHON_USE_FREELISTS 0
+  #endif
+#else
+  #define CYTHON_COMPILING_IN_PYPY 0
+  #define CYTHON_COMPILING_IN_CPYTHON 1
+  #define CYTHON_COMPILING_IN_LIMITED_API 0
+  #define CYTHON_COMPILING_IN_GRAAL 0
+  #define CYTHON_COMPILING_IN_NOGIL 0
+  #ifndef CYTHON_USE_TYPE_SLOTS
+    #define CYTHON_USE_TYPE_SLOTS 1
+  #endif
+  #ifndef CYTHON_USE_TYPE_SPECS
+    #define CYTHON_USE_TYPE_SPECS 0
+  #endif
+  #ifndef CYTHON_USE_PYTYPE_LOOKUP
+    #define CYTHON_USE_PYTYPE_LOOKUP 1
+  #endif
+  #if PY_MAJOR_VERSION < 3
+    #undef CYTHON_USE_ASYNC_SLOTS
+    #define CYTHON_USE_ASYNC_SLOTS 0
+  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
+    #define CYTHON_USE_ASYNC_SLOTS 1
+  #endif
+  #ifndef CYTHON_USE_PYLONG_INTERNALS
+    #define CYTHON_USE_PYLONG_INTERNALS 1
+  #endif
+  #ifndef CYTHON_USE_PYLIST_INTERNALS
+    #define CYTHON_USE_PYLIST_INTERNALS 1
+  #endif
+  #ifndef CYTHON_USE_UNICODE_INTERNALS
+    #define CYTHON_USE_UNICODE_INTERNALS 1
+  #endif
+  #if PY_VERSION_HEX < 0x030300F0 || PY_VERSION_HEX >= 0x030B00A2
+    #undef CYTHON_USE_UNICODE_WRITER
+    #define CYTHON_USE_UNICODE_WRITER 0
+  #elif !defined(CYTHON_USE_UNICODE_WRITER)
+    #define CYTHON_USE_UNICODE_WRITER 1
+  #endif
+  #ifndef CYTHON_AVOID_BORROWED_REFS
+    #define CYTHON_AVOID_BORROWED_REFS 0
+  #endif
+  #ifndef CYTHON_ASSUME_SAFE_MACROS
+    #define CYTHON_ASSUME_SAFE_MACROS 1
+  #endif
+  #ifndef CYTHON_UNPACK_METHODS
+    #define CYTHON_UNPACK_METHODS 1
+  #endif
+  #ifndef CYTHON_FAST_THREAD_STATE
+    #define CYTHON_FAST_THREAD_STATE 1
+  #endif
+  #ifndef CYTHON_FAST_GIL
+    #define CYTHON_FAST_GIL (PY_MAJOR_VERSION < 3 || PY_VERSION_HEX >= 0x03060000 && PY_VERSION_HEX < 0x030C00A6)
+  #endif
+  #ifndef CYTHON_METH_FASTCALL
+    #define CYTHON_METH_FASTCALL (PY_VERSION_HEX >= 0x030700A1)
+  #endif
+  #ifndef CYTHON_FAST_PYCALL
+    #define CYTHON_FAST_PYCALL 1
+  #endif
+  #ifndef CYTHON_PEP487_INIT_SUBCLASS
+    #define CYTHON_PEP487_INIT_SUBCLASS 1
+  #endif
+  #if PY_VERSION_HEX < 0x03050000
+    #undef CYTHON_PEP489_MULTI_PHASE_INIT
+    #define CYTHON_PEP489_MULTI_PHASE_INIT 0
+  #elif !defined(CYTHON_PEP489_MULTI_PHASE_INIT)
+    #define CYTHON_PEP489_MULTI_PHASE_INIT 1
+  #endif
+  #ifndef CYTHON_USE_MODULE_STATE
+    #define CYTHON_USE_MODULE_STATE 0
+  #endif
+  #if PY_VERSION_HEX < 0x030400a1
+    #undef CYTHON_USE_TP_FINALIZE
+    #define CYTHON_USE_TP_FINALIZE 0
+  #elif !defined(CYTHON_USE_TP_FINALIZE)
+    #define CYTHON_USE_TP_FINALIZE 1
+  #endif
+  #if PY_VERSION_HEX < 0x030600B1
+    #undef CYTHON_USE_DICT_VERSIONS
+    #define CYTHON_USE_DICT_VERSIONS 0
+  #elif !defined(CYTHON_USE_DICT_VERSIONS)
+    #define CYTHON_USE_DICT_VERSIONS  (PY_VERSION_HEX < 0x030C00A5)
+  #endif
+  #if PY_VERSION_HEX < 0x030700A3
+    #undef CYTHON_USE_EXC_INFO_STACK
+    #define CYTHON_USE_EXC_INFO_STACK 0
+  #elif !defined(CYTHON_USE_EXC_INFO_STACK)
+    #define CYTHON_USE_EXC_INFO_STACK 1
+  #endif
+  #ifndef CYTHON_UPDATE_DESCRIPTOR_DOC
+    #define CYTHON_UPDATE_DESCRIPTOR_DOC 1
+  #endif
+  #ifndef CYTHON_USE_FREELISTS
+    #define CYTHON_USE_FREELISTS 1
+  #endif
+#endif
+#if !defined(CYTHON_FAST_PYCCALL)
+#define CYTHON_FAST_PYCCALL  (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
+#endif
+#if !defined(CYTHON_VECTORCALL)
+#define CYTHON_VECTORCALL  (CYTHON_FAST_PYCCALL && PY_VERSION_HEX >= 0x030800B1)
+#endif
+#define CYTHON_BACKPORT_VECTORCALL (CYTHON_METH_FASTCALL && PY_VERSION_HEX < 0x030800B1)
+#if CYTHON_USE_PYLONG_INTERNALS
+  #if PY_MAJOR_VERSION < 3
+    #include "longintrepr.h"
+  #endif
+  #undef SHIFT
+  #undef BASE
+  #undef MASK
+  #ifdef SIZEOF_VOID_P
+    enum { __pyx_check_sizeof_voidp = 1 / (int)(SIZEOF_VOID_P == sizeof(void*)) };
+  #endif
+#endif
+#ifndef __has_attribute
+  #define __has_attribute(x) 0
+#endif
+#ifndef __has_cpp_attribute
+  #define __has_cpp_attribute(x) 0
+#endif
+#ifndef CYTHON_RESTRICT
+  #if defined(__GNUC__)
+    #define CYTHON_RESTRICT __restrict__
+  #elif defined(_MSC_VER) && _MSC_VER >= 1400
+    #define CYTHON_RESTRICT __restrict
+  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define CYTHON_RESTRICT restrict
+  #else
+    #define CYTHON_RESTRICT
+  #endif
+#endif
+#ifndef CYTHON_UNUSED
+  #if defined(__cplusplus)
+    /* for clang __has_cpp_attribute(maybe_unused) is true even before C++17
+     * but leads to warnings with -pedantic, since it is a C++17 feature */
+    #if ((defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) || __cplusplus >= 201703L)
+      #if __has_cpp_attribute(maybe_unused)
+        #define CYTHON_UNUSED [[maybe_unused]]
+      #endif
+    #endif
+  #endif
+#endif
+#ifndef CYTHON_UNUSED
+# if defined(__GNUC__)
+#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
+#     define CYTHON_UNUSED __attribute__ ((__unused__))
+#   else
+#     define CYTHON_UNUSED
+#   endif
+# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
+#   define CYTHON_UNUSED __attribute__ ((__unused__))
+# else
+#   define CYTHON_UNUSED
+# endif
+#endif
+#ifndef CYTHON_UNUSED_VAR
+#  if defined(__cplusplus)
+     template<class T> void CYTHON_UNUSED_VAR( const T& ) { }
+#  else
+#    define CYTHON_UNUSED_VAR(x) (void)(x)
+#  endif
+#endif
+#ifndef CYTHON_MAYBE_UNUSED_VAR
+  #define CYTHON_MAYBE_UNUSED_VAR(x) CYTHON_UNUSED_VAR(x)
+#endif
+#ifndef CYTHON_NCP_UNUSED
+# if CYTHON_COMPILING_IN_CPYTHON
+#  define CYTHON_NCP_UNUSED
+# else
+#  define CYTHON_NCP_UNUSED CYTHON_UNUSED
+# endif
+#endif
+#ifndef CYTHON_USE_CPP_STD_MOVE
+  #if defined(__cplusplus) && (\
+    __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1600))
+    #define CYTHON_USE_CPP_STD_MOVE 1
+  #else
+    #define CYTHON_USE_CPP_STD_MOVE 0
+  #endif
+#endif
+#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
+#ifdef _MSC_VER
+    #ifndef _MSC_STDINT_H_
+        #if _MSC_VER < 1300
+            typedef unsigned char     uint8_t;
+            typedef unsigned short    uint16_t;
+            typedef unsigned int      uint32_t;
+        #else
+            typedef unsigned __int8   uint8_t;
+            typedef unsigned __int16  uint16_t;
+            typedef unsigned __int32  uint32_t;
+        #endif
+    #endif
+    #if _MSC_VER < 1300
+        #ifdef _WIN64
+            typedef unsigned long long  __pyx_uintptr_t;
+        #else
+            typedef unsigned int        __pyx_uintptr_t;
+        #endif
+    #else
+        #ifdef _WIN64
+            typedef unsigned __int64    __pyx_uintptr_t;
+        #else
+            typedef unsigned __int32    __pyx_uintptr_t;
+        #endif
+    #endif
+#else
+    #include <stdint.h>
+    typedef uintptr_t  __pyx_uintptr_t;
+#endif
+#ifndef CYTHON_FALLTHROUGH
+  #if defined(__cplusplus)
+    /* for clang __has_cpp_attribute(fallthrough) is true even before C++17
+     * but leads to warnings with -pedantic, since it is a C++17 feature */
+    #if ((defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) || __cplusplus >= 201703L)
+      #if __has_cpp_attribute(fallthrough)
+        #define CYTHON_FALLTHROUGH [[fallthrough]]
+      #endif
+    #endif
+    #ifndef CYTHON_FALLTHROUGH
+      #if __has_cpp_attribute(clang::fallthrough)
+        #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
+      #elif __has_cpp_attribute(gnu::fallthrough)
+        #define CYTHON_FALLTHROUGH [[gnu::fallthrough]]
+      #endif
+    #endif
+  #endif
+  #ifndef CYTHON_FALLTHROUGH
+    #if __has_attribute(fallthrough)
+      #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
+    #else
+      #define CYTHON_FALLTHROUGH
+    #endif
+  #endif
+  #if defined(__clang__) && defined(__apple_build_version__)
+    #if __apple_build_version__ < 7000000
+      #undef  CYTHON_FALLTHROUGH
+      #define CYTHON_FALLTHROUGH
+    #endif
+  #endif
+#endif
+#ifdef __cplusplus
+  template <typename T>
+  struct __PYX_IS_UNSIGNED_IMPL {static const bool value = T(0) < T(-1);};
+  #define __PYX_IS_UNSIGNED(type) (__PYX_IS_UNSIGNED_IMPL<type>::value)
+#else
+  #define __PYX_IS_UNSIGNED(type) (((type)-1) > 0)
+#endif
+#if CYTHON_COMPILING_IN_PYPY == 1
+  #define __PYX_NEED_TP_PRINT_SLOT  (PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x030A0000)
+#else
+  #define __PYX_NEED_TP_PRINT_SLOT  (PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000)
+#endif
+#define __PYX_REINTERPRET_FUNCION(func_pointer, other_pointer) ((func_pointer)(void(*)(void))(other_pointer))
+
+#ifndef __cplusplus
+  #error "Cython files generated with the C++ option must be compiled with a C++ compiler."
+#endif
+#ifndef CYTHON_INLINE
+  #if defined(__clang__)
+    #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
+  #else
+    #define CYTHON_INLINE inline
+  #endif
+#endif
+template<typename T>
+void __Pyx_call_destructor(T& x) {
+    x.~T();
+}
+template<typename T>
+class __Pyx_FakeReference {
+  public:
+    __Pyx_FakeReference() : ptr(NULL) { }
+    __Pyx_FakeReference(const T& ref) : ptr(const_cast<T*>(&ref)) { }
+    T *operator->() { return ptr; }
+    T *operator&() { return ptr; }
+    operator T&() { return *ptr; }
+    template<typename U> bool operator ==(const U& other) const { return *ptr == other; }
+    template<typename U> bool operator !=(const U& other) const { return *ptr != other; }
+    template<typename U> bool operator==(const __Pyx_FakeReference<U>& other) const { return *ptr == *other.ptr; }
+    template<typename U> bool operator!=(const __Pyx_FakeReference<U>& other) const { return *ptr != *other.ptr; }
+  private:
+    T *ptr;
+};
+
+#define __PYX_BUILD_PY_SSIZE_T "n"
+#define CYTHON_FORMAT_SSIZE_T "z"
+#if PY_MAJOR_VERSION < 3
+  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
+  #define __Pyx_DefaultClassType PyClass_Type
+  #define __Pyx_PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#else
+  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
+  #define __Pyx_DefaultClassType PyType_Type
+#if CYTHON_COMPILING_IN_LIMITED_API
+    static CYTHON_INLINE PyObject* __Pyx_PyCode_New(int a, int p, int k, int l, int s, int f,
+                                                    PyObject *code, PyObject *c, PyObject* n, PyObject *v,
+                                                    PyObject *fv, PyObject *cell, PyObject* fn,
+                                                    PyObject *name, int fline, PyObject *lnos) {
+        PyObject *exception_table = NULL;
+        PyObject *types_module=NULL, *code_type=NULL, *result=NULL;
+        #if __PYX_LIMITED_VERSION_HEX < 0x030B0000
+        PyObject *version_info;
+        PyObject *py_minor_version = NULL;
+        #endif
+        long minor_version = 0;
+        PyObject *type, *value, *traceback;
+        PyErr_Fetch(&type, &value, &traceback);
+        #if __PYX_LIMITED_VERSION_HEX >= 0x030B0000
+        minor_version = 11;
+        #else
+        if (!(version_info = PySys_GetObject("version_info"))) goto end;
+        if (!(py_minor_version = PySequence_GetItem(version_info, 1))) goto end;
+        minor_version = PyLong_AsLong(py_minor_version);
+        Py_DECREF(py_minor_version);
+        if (minor_version == -1 && PyErr_Occurred()) goto end;
+        #endif
+        if (!(types_module = PyImport_ImportModule("types"))) goto end;
+        if (!(code_type = PyObject_GetAttrString(types_module, "CodeType"))) goto end;
+        if (minor_version <= 7) {
+            (void)p;
+            result = PyObject_CallFunction(code_type, "iiiiiOOOOOOiOO", a, k, l, s, f, code,
+                          c, n, v, fn, name, fline, lnos, fv, cell);
+        } else if (minor_version <= 10) {
+            result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOiOO", a,p, k, l, s, f, code,
+                          c, n, v, fn, name, fline, lnos, fv, cell);
+        } else {
+            if (!(exception_table = PyBytes_FromStringAndSize(NULL, 0))) goto end;
+            result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOOiOO", a,p, k, l, s, f, code,
+                          c, n, v, fn, name, name, fline, lnos, exception_table, fv, cell);
+        }
+    end:
+        Py_XDECREF(code_type);
+        Py_XDECREF(exception_table);
+        Py_XDECREF(types_module);
+        if (type) {
+            PyErr_Restore(type, value, traceback);
+        }
+        return result;
+    }
+    #ifndef CO_OPTIMIZED
+    #define CO_OPTIMIZED 0x0001
+    #endif
+    #ifndef CO_NEWLOCALS
+    #define CO_NEWLOCALS 0x0002
+    #endif
+    #ifndef CO_VARARGS
+    #define CO_VARARGS 0x0004
+    #endif
+    #ifndef CO_VARKEYWORDS
+    #define CO_VARKEYWORDS 0x0008
+    #endif
+    #ifndef CO_ASYNC_GENERATOR
+    #define CO_ASYNC_GENERATOR 0x0200
+    #endif
+    #ifndef CO_GENERATOR
+    #define CO_GENERATOR 0x0020
+    #endif
+    #ifndef CO_COROUTINE
+    #define CO_COROUTINE 0x0080
+    #endif
+#elif PY_VERSION_HEX >= 0x030B0000
+  static CYTHON_INLINE PyCodeObject* __Pyx_PyCode_New(int a, int p, int k, int l, int s, int f,
+                                                    PyObject *code, PyObject *c, PyObject* n, PyObject *v,
+                                                    PyObject *fv, PyObject *cell, PyObject* fn,
+                                                    PyObject *name, int fline, PyObject *lnos) {
+    PyCodeObject *result;
+    PyObject *empty_bytes = PyBytes_FromStringAndSize("", 0);
+    if (!empty_bytes) return NULL;
+    result =
+      #if PY_VERSION_HEX >= 0x030C0000
+        PyUnstable_Code_NewWithPosOnlyArgs
+      #else
+        PyCode_NewWithPosOnlyArgs
+      #endif
+        (a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, name, fline, lnos, empty_bytes);
+    Py_DECREF(empty_bytes);
+    return result;
+  }
+#elif PY_VERSION_HEX >= 0x030800B2 && !CYTHON_COMPILING_IN_PYPY
+  #define __Pyx_PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_NewWithPosOnlyArgs(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#else
+  #define __Pyx_PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
+          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
+#endif
+#endif
+#if PY_VERSION_HEX >= 0x030900A4 || defined(Py_IS_TYPE)
+  #define __Pyx_IS_TYPE(ob, type) Py_IS_TYPE(ob, type)
+#else
+  #define __Pyx_IS_TYPE(ob, type) (((const PyObject*)ob)->ob_type == (type))
+#endif
+#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_Is)
+  #define __Pyx_Py_Is(x, y)  Py_Is(x, y)
+#else
+  #define __Pyx_Py_Is(x, y) ((x) == (y))
+#endif
+#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsNone)
+  #define __Pyx_Py_IsNone(ob) Py_IsNone(ob)
+#else
+  #define __Pyx_Py_IsNone(ob) __Pyx_Py_Is((ob), Py_None)
+#endif
+#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsTrue)
+  #define __Pyx_Py_IsTrue(ob) Py_IsTrue(ob)
+#else
+  #define __Pyx_Py_IsTrue(ob) __Pyx_Py_Is((ob), Py_True)
+#endif
+#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsFalse)
+  #define __Pyx_Py_IsFalse(ob) Py_IsFalse(ob)
+#else
+  #define __Pyx_Py_IsFalse(ob) __Pyx_Py_Is((ob), Py_False)
+#endif
+#define __Pyx_NoneAsNull(obj)  (__Pyx_Py_IsNone(obj) ? NULL : (obj))
+#if PY_VERSION_HEX >= 0x030900F0 && !CYTHON_COMPILING_IN_PYPY
+  #define __Pyx_PyObject_GC_IsFinalized(o) PyObject_GC_IsFinalized(o)
+#else
+  #define __Pyx_PyObject_GC_IsFinalized(o) _PyGC_FINALIZED(o)
+#endif
+#ifndef CO_COROUTINE
+  #define CO_COROUTINE 0x80
+#endif
+#ifndef CO_ASYNC_GENERATOR
+  #define CO_ASYNC_GENERATOR 0x200
+#endif
+#ifndef Py_TPFLAGS_CHECKTYPES
+  #define Py_TPFLAGS_CHECKTYPES 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_INDEX
+  #define Py_TPFLAGS_HAVE_INDEX 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
+  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
+#endif
+#ifndef Py_TPFLAGS_HAVE_FINALIZE
+  #define Py_TPFLAGS_HAVE_FINALIZE 0
+#endif
+#ifndef Py_TPFLAGS_SEQUENCE
+  #define Py_TPFLAGS_SEQUENCE 0
+#endif
+#ifndef Py_TPFLAGS_MAPPING
+  #define Py_TPFLAGS_MAPPING 0
+#endif
+#ifndef METH_STACKLESS
+  #define METH_STACKLESS 0
+#endif
+#if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL)
+  #ifndef METH_FASTCALL
+     #define METH_FASTCALL 0x80
+  #endif
+  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
+  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
+                                                          Py_ssize_t nargs, PyObject *kwnames);
+#else
+  #if PY_VERSION_HEX >= 0x030d00A4
+  #  define __Pyx_PyCFunctionFast PyCFunctionFast
+  #  define __Pyx_PyCFunctionFastWithKeywords PyCFunctionFastWithKeywords
+  #else
+  #  define __Pyx_PyCFunctionFast _PyCFunctionFast
+  #  define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
+  #endif
+#endif
+#if CYTHON_METH_FASTCALL
+  #define __Pyx_METH_FASTCALL METH_FASTCALL
+  #define __Pyx_PyCFunction_FastCall __Pyx_PyCFunctionFast
+  #define __Pyx_PyCFunction_FastCallWithKeywords __Pyx_PyCFunctionFastWithKeywords
+#else
+  #define __Pyx_METH_FASTCALL METH_VARARGS
+  #define __Pyx_PyCFunction_FastCall PyCFunction
+  #define __Pyx_PyCFunction_FastCallWithKeywords PyCFunctionWithKeywords
+#endif
+#if CYTHON_VECTORCALL
+  #define __pyx_vectorcallfunc vectorcallfunc
+  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  PY_VECTORCALL_ARGUMENTS_OFFSET
+  #define __Pyx_PyVectorcall_NARGS(n)  PyVectorcall_NARGS((size_t)(n))
+#elif CYTHON_BACKPORT_VECTORCALL
+  typedef PyObject *(*__pyx_vectorcallfunc)(PyObject *callable, PyObject *const *args,
+                                            size_t nargsf, PyObject *kwnames);
+  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  ((size_t)1 << (8 * sizeof(size_t) - 1))
+  #define __Pyx_PyVectorcall_NARGS(n)  ((Py_ssize_t)(((size_t)(n)) & ~__Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET))
+#else
+  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  0
+  #define __Pyx_PyVectorcall_NARGS(n)  ((Py_ssize_t)(n))
+#endif
+#if PY_MAJOR_VERSION >= 0x030900B1
+#define __Pyx_PyCFunction_CheckExact(func)  PyCFunction_CheckExact(func)
+#else
+#define __Pyx_PyCFunction_CheckExact(func)  PyCFunction_Check(func)
+#endif
+#define __Pyx_CyOrPyCFunction_Check(func)  PyCFunction_Check(func)
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func)  (((PyCFunctionObject*)(func))->m_ml->ml_meth)
+#elif !CYTHON_COMPILING_IN_LIMITED_API
+#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func)  PyCFunction_GET_FUNCTION(func)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __Pyx_CyOrPyCFunction_GET_FLAGS(func)  (((PyCFunctionObject*)(func))->m_ml->ml_flags)
+static CYTHON_INLINE PyObject* __Pyx_CyOrPyCFunction_GET_SELF(PyObject *func) {
+    return (__Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_STATIC) ? NULL : ((PyCFunctionObject*)func)->m_self;
+}
+#endif
+static CYTHON_INLINE int __Pyx__IsSameCFunction(PyObject *func, void *cfunc) {
+#if CYTHON_COMPILING_IN_LIMITED_API
+    return PyCFunction_Check(func) && PyCFunction_GetFunction(func) == (PyCFunction) cfunc;
+#else
+    return PyCFunction_Check(func) && PyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc;
+#endif
+}
+#define __Pyx_IsSameCFunction(func, cfunc)   __Pyx__IsSameCFunction(func, cfunc)
+#if __PYX_LIMITED_VERSION_HEX < 0x030900B1
+  #define __Pyx_PyType_FromModuleAndSpec(m, s, b)  ((void)m, PyType_FromSpecWithBases(s, b))
+  typedef PyObject *(*__Pyx_PyCMethod)(PyObject *, PyTypeObject *, PyObject *const *, size_t, PyObject *);
+#else
+  #define __Pyx_PyType_FromModuleAndSpec(m, s, b)  PyType_FromModuleAndSpec(m, s, b)
+  #define __Pyx_PyCMethod  PyCMethod
+#endif
+#ifndef METH_METHOD
+  #define METH_METHOD 0x200
+#endif
+#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
+  #define PyObject_Malloc(s)   PyMem_Malloc(s)
+  #define PyObject_Free(p)     PyMem_Free(p)
+  #define PyObject_Realloc(p)  PyMem_Realloc(p)
+#endif
+#if CYTHON_COMPILING_IN_LIMITED_API
+  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
+  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)
+#else
+  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
+  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
+#endif
+#if CYTHON_COMPILING_IN_LIMITED_API
+  #define __Pyx_PyThreadState_Current PyThreadState_Get()
+#elif !CYTHON_FAST_THREAD_STATE
+  #define __Pyx_PyThreadState_Current PyThreadState_GET()
+#elif PY_VERSION_HEX >= 0x030d00A1
+  #define __Pyx_PyThreadState_Current PyThreadState_GetUnchecked()
+#elif PY_VERSION_HEX >= 0x03060000
+  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
+#elif PY_VERSION_HEX >= 0x03000000
+  #define __Pyx_PyThreadState_Current PyThreadState_GET()
+#else
+  #define __Pyx_PyThreadState_Current _PyThreadState_Current
+#endif
+#if CYTHON_COMPILING_IN_LIMITED_API
+static CYTHON_INLINE void *__Pyx_PyModule_GetState(PyObject *op)
+{
+    void *result;
+    result = PyModule_GetState(op);
+    if (!result)
+        Py_FatalError("Couldn't find the module state");
+    return result;
+}
+#endif
+#define __Pyx_PyObject_GetSlot(obj, name, func_ctype)  __Pyx_PyType_GetSlot(Py_TYPE(obj), name, func_ctype)
+#if CYTHON_COMPILING_IN_LIMITED_API
+  #define __Pyx_PyType_GetSlot(type, name, func_ctype)  ((func_ctype) PyType_GetSlot((type), Py_##name))
+#else
+  #define __Pyx_PyType_GetSlot(type, name, func_ctype)  ((type)->name)
+#endif
+#if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT)
+#include "pythread.h"
+#define Py_tss_NEEDS_INIT 0
+typedef int Py_tss_t;
+static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
+  *key = PyThread_create_key();
+  return 0;
+}
+static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) {
+  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
+  *key = Py_tss_NEEDS_INIT;
+  return key;
+}
+static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
+  PyObject_Free(key);
+}
+static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
+  return *key != Py_tss_NEEDS_INIT;
+}
+static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
+  PyThread_delete_key(*key);
+  *key = Py_tss_NEEDS_INIT;
+}
+static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
+  return PyThread_set_key_value(*key, value);
+}
+static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
+  return PyThread_get_key_value(*key);
+}
+#endif
+#if PY_MAJOR_VERSION < 3
+    #if CYTHON_COMPILING_IN_PYPY
+        #if PYPY_VERSION_NUM < 0x07030600
+            #if defined(__cplusplus) && __cplusplus >= 201402L
+                [[deprecated("`with nogil:` inside a nogil function will not release the GIL in PyPy2 < 7.3.6")]]
+            #elif defined(__GNUC__) || defined(__clang__)
+                __attribute__ ((__deprecated__("`with nogil:` inside a nogil function will not release the GIL in PyPy2 < 7.3.6")))
+            #elif defined(_MSC_VER)
+                __declspec(deprecated("`with nogil:` inside a nogil function will not release the GIL in PyPy2 < 7.3.6"))
+            #endif
+            static CYTHON_INLINE int PyGILState_Check(void) {
+                return 0;
+            }
+        #else  // PYPY_VERSION_NUM < 0x07030600
+        #endif  // PYPY_VERSION_NUM < 0x07030600
+    #else
+        static CYTHON_INLINE int PyGILState_Check(void) {
+            PyThreadState * tstate = _PyThreadState_Current;
+            return tstate && (tstate == PyGILState_GetThisThreadState());
+        }
+    #endif
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030d0000 || defined(_PyDict_NewPresized)
+#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
+#else
+#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
+#endif
+#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
+#else
+  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
+  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX > 0x030600B4 && PY_VERSION_HEX < 0x030d0000 && CYTHON_USE_UNICODE_INTERNALS
+#define __Pyx_PyDict_GetItemStrWithError(dict, name)  _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
+static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStr(PyObject *dict, PyObject *name) {
+    PyObject *res = __Pyx_PyDict_GetItemStrWithError(dict, name);
+    if (res == NULL) PyErr_Clear();
+    return res;
+}
+#elif PY_MAJOR_VERSION >= 3 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07020000)
+#define __Pyx_PyDict_GetItemStrWithError  PyDict_GetItemWithError
+#define __Pyx_PyDict_GetItemStr           PyDict_GetItem
+#else
+static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStrWithError(PyObject *dict, PyObject *name) {
+#if CYTHON_COMPILING_IN_PYPY
+    return PyDict_GetItem(dict, name);
+#else
+    PyDictEntry *ep;
+    PyDictObject *mp = (PyDictObject*) dict;
+    long hash = ((PyStringObject *) name)->ob_shash;
+    assert(hash != -1);
+    ep = (mp->ma_lookup)(mp, name, hash);
+    if (ep == NULL) {
+        return NULL;
+    }
+    return ep->me_value;
+#endif
+}
+#define __Pyx_PyDict_GetItemStr           PyDict_GetItem
+#endif
+#if CYTHON_USE_TYPE_SLOTS
+  #define __Pyx_PyType_GetFlags(tp)   (((PyTypeObject *)tp)->tp_flags)
+  #define __Pyx_PyType_HasFeature(type, feature)  ((__Pyx_PyType_GetFlags(type) & (feature)) != 0)
+  #define __Pyx_PyObject_GetIterNextFunc(obj)  (Py_TYPE(obj)->tp_iternext)
+#else
+  #define __Pyx_PyType_GetFlags(tp)   (PyType_GetFlags((PyTypeObject *)tp))
+  #define __Pyx_PyType_HasFeature(type, feature)  PyType_HasFeature(type, feature)
+  #define __Pyx_PyObject_GetIterNextFunc(obj)  PyIter_Next
+#endif
+#if CYTHON_COMPILING_IN_LIMITED_API
+  #define __Pyx_SetItemOnTypeDict(tp, k, v) PyObject_GenericSetAttr((PyObject*)tp, k, v)
+#else
+  #define __Pyx_SetItemOnTypeDict(tp, k, v) PyDict_SetItem(tp->tp_dict, k, v)
+#endif
+#if CYTHON_USE_TYPE_SPECS && PY_VERSION_HEX >= 0x03080000
+#define __Pyx_PyHeapTypeObject_GC_Del(obj)  {\
+    PyTypeObject *type = Py_TYPE((PyObject*)obj);\
+    assert(__Pyx_PyType_HasFeature(type, Py_TPFLAGS_HEAPTYPE));\
+    PyObject_GC_Del(obj);\
+    Py_DECREF(type);\
+}
+#else
+#define __Pyx_PyHeapTypeObject_GC_Del(obj)  PyObject_GC_Del(obj)
+#endif
+#if CYTHON_COMPILING_IN_LIMITED_API
+  #define CYTHON_PEP393_ENABLED 1
+  #define __Pyx_PyUnicode_READY(op)       (0)
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GetLength(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_ReadChar(u, i)
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((void)u, 1114111U)
+  #define __Pyx_PyUnicode_KIND(u)         ((void)u, (0))
+  #define __Pyx_PyUnicode_DATA(u)         ((void*)u)
+  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)k, PyUnicode_ReadChar((PyObject*)(d), i))
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GetLength(u))
+#elif PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
+  #define CYTHON_PEP393_ENABLED 1
+  #if PY_VERSION_HEX >= 0x030C0000
+    #define __Pyx_PyUnicode_READY(op)       (0)
+  #else
+    #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
+                                                0 : _PyUnicode_Ready((PyObject *)(op)))
+  #endif
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
+  #define __Pyx_PyUnicode_KIND(u)         ((int)PyUnicode_KIND(u))
+  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
+  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
+  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, (Py_UCS4) ch)
+  #if PY_VERSION_HEX >= 0x030C0000
+    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_LENGTH(u))
+  #else
+    #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000
+    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length))
+    #else
+    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
+    #endif
+  #endif
+#else
+  #define CYTHON_PEP393_ENABLED 0
+  #define PyUnicode_1BYTE_KIND  1
+  #define PyUnicode_2BYTE_KIND  2
+  #define PyUnicode_4BYTE_KIND  4
+  #define __Pyx_PyUnicode_READY(op)       (0)
+  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
+  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
+  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((sizeof(Py_UNICODE) == 2) ? 65535U : 1114111U)
+  #define __Pyx_PyUnicode_KIND(u)         ((int)sizeof(Py_UNICODE))
+  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
+  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
+  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  (((void)(k)), ((Py_UNICODE*)d)[i] = (Py_UNICODE) ch)
+  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))
+#endif
+#if CYTHON_COMPILING_IN_PYPY
+  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
+#else
+  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
+  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
+      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
+#endif
+#if CYTHON_COMPILING_IN_PYPY
+  #if !defined(PyUnicode_DecodeUnicodeEscape)
+    #define PyUnicode_DecodeUnicodeEscape(s, size, errors)  PyUnicode_Decode(s, size, "unicode_escape", errors)
+  #endif
+  #if !defined(PyUnicode_Contains) || (PY_MAJOR_VERSION == 2 && PYPY_VERSION_NUM < 0x07030500)
+    #undef PyUnicode_Contains
+    #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
+  #endif
+  #if !defined(PyByteArray_Check)
+    #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
+  #endif
+  #if !defined(PyObject_Format)
+    #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
+  #endif
+#endif
+#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
+#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
+#else
+  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
+#endif
+#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
+  #define PyObject_ASCII(o)            PyObject_Repr(o)
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBaseString_Type            PyUnicode_Type
+  #define PyStringObject               PyUnicodeObject
+  #define PyString_Type                PyUnicode_Type
+  #define PyString_Check               PyUnicode_Check
+  #define PyString_CheckExact          PyUnicode_CheckExact
+#ifndef PyObject_Unicode
+  #define PyObject_Unicode             PyObject_Str
+#endif
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
+  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
+#else
+  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
+  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON
+  #define __Pyx_PySequence_ListKeepNew(obj)\
+    (likely(PyList_CheckExact(obj) && Py_REFCNT(obj) == 1) ? __Pyx_NewRef(obj) : PySequence_List(obj))
+#else
+  #define __Pyx_PySequence_ListKeepNew(obj)  PySequence_List(obj)
+#endif
+#ifndef PySet_CheckExact
+  #define PySet_CheckExact(obj)        __Pyx_IS_TYPE(obj, &PySet_Type)
+#endif
+#if PY_VERSION_HEX >= 0x030900A4
+  #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt)
+  #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size)
+#else
+  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
+  #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size)
+#endif
+#if CYTHON_ASSUME_SAFE_MACROS
+  #define __Pyx_PySequence_ITEM(o, i) PySequence_ITEM(o, i)
+  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
+  #define __Pyx_PyTuple_SET_ITEM(o, i, v) (PyTuple_SET_ITEM(o, i, v), (0))
+  #define __Pyx_PyList_SET_ITEM(o, i, v) (PyList_SET_ITEM(o, i, v), (0))
+  #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_GET_SIZE(o)
+  #define __Pyx_PyList_GET_SIZE(o) PyList_GET_SIZE(o)
+  #define __Pyx_PySet_GET_SIZE(o) PySet_GET_SIZE(o)
+  #define __Pyx_PyBytes_GET_SIZE(o) PyBytes_GET_SIZE(o)
+  #define __Pyx_PyByteArray_GET_SIZE(o) PyByteArray_GET_SIZE(o)
+#else
+  #define __Pyx_PySequence_ITEM(o, i) PySequence_GetItem(o, i)
+  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
+  #define __Pyx_PyTuple_SET_ITEM(o, i, v) PyTuple_SetItem(o, i, v)
+  #define __Pyx_PyList_SET_ITEM(o, i, v) PyList_SetItem(o, i, v)
+  #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_Size(o)
+  #define __Pyx_PyList_GET_SIZE(o) PyList_Size(o)
+  #define __Pyx_PySet_GET_SIZE(o) PySet_Size(o)
+  #define __Pyx_PyBytes_GET_SIZE(o) PyBytes_Size(o)
+  #define __Pyx_PyByteArray_GET_SIZE(o) PyByteArray_Size(o)
+#endif
+#if __PYX_LIMITED_VERSION_HEX >= 0x030d00A1
+  #define __Pyx_PyImport_AddModuleRef(name) PyImport_AddModuleRef(name)
+#else
+  static CYTHON_INLINE PyObject *__Pyx_PyImport_AddModuleRef(const char *name) {
+      PyObject *module = PyImport_AddModule(name);
+      Py_XINCREF(module);
+      return module;
+  }
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyIntObject                  PyLongObject
+  #define PyInt_Type                   PyLong_Type
+  #define PyInt_Check(op)              PyLong_Check(op)
+  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
+  #define __Pyx_Py3Int_Check(op)       PyLong_Check(op)
+  #define __Pyx_Py3Int_CheckExact(op)  PyLong_CheckExact(op)
+  #define PyInt_FromString             PyLong_FromString
+  #define PyInt_FromUnicode            PyLong_FromUnicode
+  #define PyInt_FromLong               PyLong_FromLong
+  #define PyInt_FromSize_t             PyLong_FromSize_t
+  #define PyInt_FromSsize_t            PyLong_FromSsize_t
+  #define PyInt_AsLong                 PyLong_AsLong
+  #define PyInt_AS_LONG                PyLong_AS_LONG
+  #define PyInt_AsSsize_t              PyLong_AsSsize_t
+  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
+  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
+  #define PyNumber_Int                 PyNumber_Long
+#else
+  #define __Pyx_Py3Int_Check(op)       (PyLong_Check(op) || PyInt_Check(op))
+  #define __Pyx_Py3Int_CheckExact(op)  (PyLong_CheckExact(op) || PyInt_CheckExact(op))
+#endif
+#if PY_MAJOR_VERSION >= 3
+  #define PyBoolObject                 PyLongObject
+#endif
+#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
+  #ifndef PyUnicode_InternFromString
+    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
+  #endif
+#endif
+#if PY_VERSION_HEX < 0x030200A4
+  typedef long Py_hash_t;
+  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
+  #define __Pyx_PyInt_AsHash_t   __Pyx_PyIndex_AsHash_t
+#else
+  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
+  #define __Pyx_PyInt_AsHash_t   __Pyx_PyIndex_AsSsize_t
+#endif
+#if CYTHON_USE_ASYNC_SLOTS
+  #if PY_VERSION_HEX >= 0x030500B1
+    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
+    #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
+  #else
+    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
+  #endif
+#else
+  #define __Pyx_PyType_AsAsync(obj) NULL
+#endif
+#ifndef __Pyx_PyAsyncMethodsStruct
+    typedef struct {
+        unaryfunc am_await;
+        unaryfunc am_aiter;
+        unaryfunc am_anext;
+    } __Pyx_PyAsyncMethodsStruct;
+#endif
+
+#if defined(_WIN32) || defined(WIN32) || defined(MS_WINDOWS)
+  #if !defined(_USE_MATH_DEFINES)
+    #define _USE_MATH_DEFINES
+  #endif
+#endif
+#include <math.h>
+#ifdef NAN
+#define __PYX_NAN() ((float) NAN)
+#else
+static CYTHON_INLINE float __PYX_NAN() {
+  float value;
+  memset(&value, 0xFF, sizeof(value));
+  return value;
+}
+#endif
+#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
+#define __Pyx_truncl trunc
+#else
+#define __Pyx_truncl truncl
+#endif
+
+#define __PYX_MARK_ERR_POS(f_index, lineno) \
+    { __pyx_filename = __pyx_f[f_index]; (void)__pyx_filename; __pyx_lineno = lineno; (void)__pyx_lineno; __pyx_clineno = __LINE__;  (void)__pyx_clineno; }
+#define __PYX_ERR(f_index, lineno, Ln_error) \
+    { __PYX_MARK_ERR_POS(f_index, lineno) goto Ln_error; }
+
+#ifdef CYTHON_EXTERN_C
+    #undef __PYX_EXTERN_C
+    #define __PYX_EXTERN_C CYTHON_EXTERN_C
+#elif defined(__PYX_EXTERN_C)
+    #ifdef _MSC_VER
+    #pragma message ("Please do not define the '__PYX_EXTERN_C' macro externally. Use 'CYTHON_EXTERN_C' instead.")
+    #else
+    #warning Please do not define the '__PYX_EXTERN_C' macro externally. Use 'CYTHON_EXTERN_C' instead.
+    #endif
+#else
+    #define __PYX_EXTERN_C extern "C++"
+#endif
+
+#define __PYX_HAVE__onlinemid__onlinemid__runningstats
+#define __PYX_HAVE_API__onlinemid__onlinemid__runningstats
+/* Early includes */
+#include <string.h>
+#include <stdio.h>
+
+    /* Using NumPy API declarations from "numpy/__init__.cython-30.pxd" */
+    
+#include "numpy/arrayobject.h"
+#include "numpy/ndarrayobject.h"
+#include "numpy/ndarraytypes.h"
+#include "numpy/arrayscalars.h"
+#include "numpy/ufuncobject.h"
+#include <stdint.h>
+#include "runningstats_impl.h"
+#ifdef _OPENMP
+#include <omp.h>
+#endif /* _OPENMP */
+
+#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
+#define CYTHON_WITHOUT_ASSERTIONS
+#endif
+
+typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
+                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;
+
+#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
+#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
+#define __PYX_DEFAULT_STRING_ENCODING ""
+#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
+#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#define __Pyx_uchar_cast(c) ((unsigned char)c)
+#define __Pyx_long_cast(x) ((long)x)
+#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
+    (sizeof(type) < sizeof(Py_ssize_t))  ||\
+    (sizeof(type) > sizeof(Py_ssize_t) &&\
+          likely(v < (type)PY_SSIZE_T_MAX ||\
+                 v == (type)PY_SSIZE_T_MAX)  &&\
+          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
+                                v == (type)PY_SSIZE_T_MIN)))  ||\
+    (sizeof(type) == sizeof(Py_ssize_t) &&\
+          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
+                               v == (type)PY_SSIZE_T_MAX)))  )
+static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
+    return (size_t) i < (size_t) limit;
+}
+#if defined (__cplusplus) && __cplusplus >= 201103L
+    #include <cstdlib>
+    #define __Pyx_sst_abs(value) std::abs(value)
+#elif SIZEOF_INT >= SIZEOF_SIZE_T
+    #define __Pyx_sst_abs(value) abs(value)
+#elif SIZEOF_LONG >= SIZEOF_SIZE_T
+    #define __Pyx_sst_abs(value) labs(value)
+#elif defined (_MSC_VER)
+    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
+#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
+    #define __Pyx_sst_abs(value) llabs(value)
+#elif defined (__GNUC__)
+    #define __Pyx_sst_abs(value) __builtin_llabs(value)
+#else
+    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
+#endif
+static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s);
+static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
+static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
+static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char*);
+#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
+#define __Pyx_PyBytes_FromString        PyBytes_FromString
+#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
+#if PY_MAJOR_VERSION < 3
+    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
+#else
+    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
+    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
+#endif
+#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
+#define __Pyx_PyObject_AsWritableString(s)    ((char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
+#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
+#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
+#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
+#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
+#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
+#define __Pyx_PyUnicode_FromOrdinal(o)       PyUnicode_FromOrdinal((int)o)
+#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
+#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
+#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
+static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
+static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
+#define __Pyx_PySequence_Tuple(obj)\
+    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
+static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject*);
+#if CYTHON_ASSUME_SAFE_MACROS
+#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
+#else
+#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
+#endif
+#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
+#if PY_MAJOR_VERSION >= 3
+#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
+#else
+#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
+#endif
+#if CYTHON_USE_PYLONG_INTERNALS
+  #if PY_VERSION_HEX >= 0x030C00A7
+  #ifndef _PyLong_SIGN_MASK
+    #define _PyLong_SIGN_MASK 3
+  #endif
+  #ifndef _PyLong_NON_SIZE_BITS
+    #define _PyLong_NON_SIZE_BITS 3
+  #endif
+  #define __Pyx_PyLong_Sign(x)  (((PyLongObject*)x)->long_value.lv_tag & _PyLong_SIGN_MASK)
+  #define __Pyx_PyLong_IsNeg(x)  ((__Pyx_PyLong_Sign(x) & 2) != 0)
+  #define __Pyx_PyLong_IsNonNeg(x)  (!__Pyx_PyLong_IsNeg(x))
+  #define __Pyx_PyLong_IsZero(x)  (__Pyx_PyLong_Sign(x) & 1)
+  #define __Pyx_PyLong_IsPos(x)  (__Pyx_PyLong_Sign(x) == 0)
+  #define __Pyx_PyLong_CompactValueUnsigned(x)  (__Pyx_PyLong_Digits(x)[0])
+  #define __Pyx_PyLong_DigitCount(x)  ((Py_ssize_t) (((PyLongObject*)x)->long_value.lv_tag >> _PyLong_NON_SIZE_BITS))
+  #define __Pyx_PyLong_SignedDigitCount(x)\
+        ((1 - (Py_ssize_t) __Pyx_PyLong_Sign(x)) * __Pyx_PyLong_DigitCount(x))
+  #if defined(PyUnstable_Long_IsCompact) && defined(PyUnstable_Long_CompactValue)
+    #define __Pyx_PyLong_IsCompact(x)     PyUnstable_Long_IsCompact((PyLongObject*) x)
+    #define __Pyx_PyLong_CompactValue(x)  PyUnstable_Long_CompactValue((PyLongObject*) x)
+  #else
+    #define __Pyx_PyLong_IsCompact(x)     (((PyLongObject*)x)->long_value.lv_tag < (2 << _PyLong_NON_SIZE_BITS))
+    #define __Pyx_PyLong_CompactValue(x)  ((1 - (Py_ssize_t) __Pyx_PyLong_Sign(x)) * (Py_ssize_t) __Pyx_PyLong_Digits(x)[0])
+  #endif
+  typedef Py_ssize_t  __Pyx_compact_pylong;
+  typedef size_t  __Pyx_compact_upylong;
+  #else
+  #define __Pyx_PyLong_IsNeg(x)  (Py_SIZE(x) < 0)
+  #define __Pyx_PyLong_IsNonNeg(x)  (Py_SIZE(x) >= 0)
+  #define __Pyx_PyLong_IsZero(x)  (Py_SIZE(x) == 0)
+  #define __Pyx_PyLong_IsPos(x)  (Py_SIZE(x) > 0)
+  #define __Pyx_PyLong_CompactValueUnsigned(x)  ((Py_SIZE(x) == 0) ? 0 : __Pyx_PyLong_Digits(x)[0])
+  #define __Pyx_PyLong_DigitCount(x)  __Pyx_sst_abs(Py_SIZE(x))
+  #define __Pyx_PyLong_SignedDigitCount(x)  Py_SIZE(x)
+  #define __Pyx_PyLong_IsCompact(x)  (Py_SIZE(x) == 0 || Py_SIZE(x) == 1 || Py_SIZE(x) == -1)
+  #define __Pyx_PyLong_CompactValue(x)\
+        ((Py_SIZE(x) == 0) ? (sdigit) 0 : ((Py_SIZE(x) < 0) ? -(sdigit)__Pyx_PyLong_Digits(x)[0] : (sdigit)__Pyx_PyLong_Digits(x)[0]))
+  typedef sdigit  __Pyx_compact_pylong;
+  typedef digit  __Pyx_compact_upylong;
+  #endif
+  #if PY_VERSION_HEX >= 0x030C00A5
+  #define __Pyx_PyLong_Digits(x)  (((PyLongObject*)x)->long_value.ob_digit)
+  #else
+  #define __Pyx_PyLong_Digits(x)  (((PyLongObject*)x)->ob_digit)
+  #endif
+#endif
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+#include <string.h>
+static int __Pyx_sys_getdefaultencoding_not_ascii;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    PyObject* ascii_chars_u = NULL;
+    PyObject* ascii_chars_b = NULL;
+    const char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    if (strcmp(default_encoding_c, "ascii") == 0) {
+        __Pyx_sys_getdefaultencoding_not_ascii = 0;
+    } else {
+        char ascii_chars[128];
+        int c;
+        for (c = 0; c < 128; c++) {
+            ascii_chars[c] = (char) c;
+        }
+        __Pyx_sys_getdefaultencoding_not_ascii = 1;
+        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
+        if (!ascii_chars_u) goto bad;
+        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
+        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
+            PyErr_Format(
+                PyExc_ValueError,
+                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
+                default_encoding_c);
+            goto bad;
+        }
+        Py_DECREF(ascii_chars_u);
+        Py_DECREF(ascii_chars_b);
+    }
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    Py_XDECREF(ascii_chars_u);
+    Py_XDECREF(ascii_chars_b);
+    return -1;
+}
+#endif
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
+#else
+#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
+#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+#include <string.h>
+static char* __PYX_DEFAULT_STRING_ENCODING;
+static int __Pyx_init_sys_getdefaultencoding_params(void) {
+    PyObject* sys;
+    PyObject* default_encoding = NULL;
+    char* default_encoding_c;
+    sys = PyImport_ImportModule("sys");
+    if (!sys) goto bad;
+    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
+    Py_DECREF(sys);
+    if (!default_encoding) goto bad;
+    default_encoding_c = PyBytes_AsString(default_encoding);
+    if (!default_encoding_c) goto bad;
+    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
+    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
+    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
+    Py_DECREF(default_encoding);
+    return 0;
+bad:
+    Py_XDECREF(default_encoding);
+    return -1;
+}
+#endif
+#endif
+
+
+/* Test for GCC > 2.95 */
+#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
+  #define likely(x)   __builtin_expect(!!(x), 1)
+  #define unlikely(x) __builtin_expect(!!(x), 0)
+#else /* !__GNUC__ or GCC < 2.95 */
+  #define likely(x)   (x)
+  #define unlikely(x) (x)
+#endif /* __GNUC__ */
+static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
+
+#if !CYTHON_USE_MODULE_STATE
+static PyObject *__pyx_m = NULL;
+#endif
+static int __pyx_lineno;
+static int __pyx_clineno = 0;
+static const char * __pyx_cfilenm = __FILE__;
+static const char *__pyx_filename;
+
+/* Header.proto */
+#if !defined(CYTHON_CCOMPLEX)
+  #if defined(__cplusplus)
+    #define CYTHON_CCOMPLEX 1
+  #elif (defined(_Complex_I) && !defined(_MSC_VER)) || ((defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L) && !defined(__STDC_NO_COMPLEX__) && !defined(_MSC_VER))
+    #define CYTHON_CCOMPLEX 1
+  #else
+    #define CYTHON_CCOMPLEX 0
+  #endif
+#endif
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #include <complex>
+  #else
+    #include <complex.h>
+  #endif
+#endif
+#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
+  #undef _Complex_I
+  #define _Complex_I 1.0fj
+#endif
+
+/* #### Code section: filename_table ### */
+
+static const char *__pyx_f[] = {
+  "__init__.cython-30.pxd",
+  "src/onlinemid/runningstats/runningstats.pyx",
+  "type.pxd",
+};
+/* #### Code section: utility_code_proto_before_types ### */
+/* ForceInitThreads.proto */
+#ifndef __PYX_FORCE_INIT_THREADS
+  #define __PYX_FORCE_INIT_THREADS 0
+#endif
+
+/* BufferFormatStructs.proto */
+struct __Pyx_StructField_;
+#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
+typedef struct {
+  const char* name;
+  struct __Pyx_StructField_* fields;
+  size_t size;
+  size_t arraysize[8];
+  int ndim;
+  char typegroup;
+  char is_unsigned;
+  int flags;
+} __Pyx_TypeInfo;
+typedef struct __Pyx_StructField_ {
+  __Pyx_TypeInfo* type;
+  const char* name;
+  size_t offset;
+} __Pyx_StructField;
+typedef struct {
+  __Pyx_StructField* field;
+  size_t parent_offset;
+} __Pyx_BufFmt_StackElem;
+typedef struct {
+  __Pyx_StructField root;
+  __Pyx_BufFmt_StackElem* head;
+  size_t fmt_offset;
+  size_t new_count, enc_count;
+  size_t struct_alignment;
+  int is_complex;
+  char enc_type;
+  char new_packmode;
+  char enc_packmode;
+  char is_valid_array;
+} __Pyx_BufFmt_Context;
+
+/* #### Code section: numeric_typedefs ### */
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":770
+ * # in Cython to enable them only on the right systems.
+ * 
+ * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ */
+typedef npy_int8 __pyx_t_5numpy_int8_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":771
+ * 
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t
+ */
+typedef npy_int16 __pyx_t_5numpy_int16_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":772
+ * ctypedef npy_int8       int8_t
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_int64      int64_t
+ * #ctypedef npy_int96      int96_t
+ */
+typedef npy_int32 __pyx_t_5numpy_int32_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":773
+ * ctypedef npy_int16      int16_t
+ * ctypedef npy_int32      int32_t
+ * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_int96      int96_t
+ * #ctypedef npy_int128     int128_t
+ */
+typedef npy_int64 __pyx_t_5numpy_int64_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":777
+ * #ctypedef npy_int128     int128_t
+ * 
+ * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ */
+typedef npy_uint8 __pyx_t_5numpy_uint8_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":778
+ * 
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t
+ */
+typedef npy_uint16 __pyx_t_5numpy_uint16_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":779
+ * ctypedef npy_uint8      uint8_t
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uint64     uint64_t
+ * #ctypedef npy_uint96     uint96_t
+ */
+typedef npy_uint32 __pyx_t_5numpy_uint32_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":780
+ * ctypedef npy_uint16     uint16_t
+ * ctypedef npy_uint32     uint32_t
+ * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_uint96     uint96_t
+ * #ctypedef npy_uint128    uint128_t
+ */
+typedef npy_uint64 __pyx_t_5numpy_uint64_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":784
+ * #ctypedef npy_uint128    uint128_t
+ * 
+ * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_float64    float64_t
+ * #ctypedef npy_float80    float80_t
+ */
+typedef npy_float32 __pyx_t_5numpy_float32_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":785
+ * 
+ * ctypedef npy_float32    float32_t
+ * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
+ * #ctypedef npy_float80    float80_t
+ * #ctypedef npy_float128   float128_t
+ */
+typedef npy_float64 __pyx_t_5numpy_float64_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":792
+ * ctypedef double complex complex128_t
+ * 
+ * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ */
+typedef npy_longlong __pyx_t_5numpy_longlong_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":793
+ * 
+ * ctypedef npy_longlong   longlong_t
+ * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_intp       intp_t
+ */
+typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":795
+ * ctypedef npy_ulonglong  ulonglong_t
+ * 
+ * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_uintp      uintp_t
+ * 
+ */
+typedef npy_intp __pyx_t_5numpy_intp_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":796
+ * 
+ * ctypedef npy_intp       intp_t
+ * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef npy_double     float_t
+ */
+typedef npy_uintp __pyx_t_5numpy_uintp_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":798
+ * ctypedef npy_uintp      uintp_t
+ * 
+ * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t
+ */
+typedef npy_double __pyx_t_5numpy_float_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":799
+ * 
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
+ * ctypedef npy_longdouble longdouble_t
+ * 
+ */
+typedef npy_double __pyx_t_5numpy_double_t;
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":800
+ * ctypedef npy_double     float_t
+ * ctypedef npy_double     double_t
+ * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
+ * 
+ * ctypedef float complex       cfloat_t
+ */
+typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
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+/* Declarations.proto */
+#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+  #ifdef __cplusplus
+    typedef ::std::complex< float > __pyx_t_float_complex;
+  #else
+    typedef float _Complex __pyx_t_float_complex;
+  #endif
+#else
+    typedef struct { float real, imag; } __pyx_t_float_complex;
+#endif
+static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);
+
+/* Declarations.proto */
+#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+  #ifdef __cplusplus
+    typedef ::std::complex< double > __pyx_t_double_complex;
+  #else
+    typedef double _Complex __pyx_t_double_complex;
+  #endif
+#else
+    typedef struct { double real, imag; } __pyx_t_double_complex;
+#endif
+static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);
+
+/* Declarations.proto */
+#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+  #ifdef __cplusplus
+    typedef ::std::complex< long double > __pyx_t_long_double_complex;
+  #else
+    typedef long double _Complex __pyx_t_long_double_complex;
+  #endif
+#else
+    typedef struct { long double real, imag; } __pyx_t_long_double_complex;
+#endif
+static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double, long double);
+
+/* #### Code section: type_declarations ### */
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+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":1096
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+ * ctypedef int (*NpyIter_IterNextFunc)(NpyIter* it) noexcept nogil             # <<<<<<<<<<<<<<
+ * ctypedef void (*NpyIter_GetMultiIndexFunc)(NpyIter* it, npy_intp* outcoords) noexcept nogil
+ * 
+ */
+typedef int (*__pyx_t_5numpy_NpyIter_IterNextFunc)(NpyIter *);
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":1097
+ * # Iterator API added in v1.6
+ * ctypedef int (*NpyIter_IterNextFunc)(NpyIter* it) noexcept nogil
+ * ctypedef void (*NpyIter_GetMultiIndexFunc)(NpyIter* it, npy_intp* outcoords) noexcept nogil             # <<<<<<<<<<<<<<
+ * 
+ * cdef extern from "numpy/arrayobject.h":
+ */
+typedef void (*__pyx_t_5numpy_NpyIter_GetMultiIndexFunc)(NpyIter *, npy_intp *);
+/* #### Code section: utility_code_proto ### */
+
+/* --- Runtime support code (head) --- */
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+  #define __Pyx_GOTREF(r)  __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), (__LINE__))
+  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), (__LINE__))
+  #define __Pyx_XINCREF(r)  do { if((r) == NULL); else {__Pyx_INCREF(r); }} while(0)
+  #define __Pyx_XDECREF(r)  do { if((r) == NULL); else {__Pyx_DECREF(r); }} while(0)
+  #define __Pyx_XGOTREF(r)  do { if((r) == NULL); else {__Pyx_GOTREF(r); }} while(0)
+  #define __Pyx_XGIVEREF(r) do { if((r) == NULL); else {__Pyx_GIVEREF(r);}} while(0)
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+  #define __Pyx_RefNannyDeclarations
+  #define __Pyx_RefNannySetupContext(name, acquire_gil)
+  #define __Pyx_RefNannyFinishContextNogil()
+  #define __Pyx_RefNannyFinishContext()
+  #define __Pyx_INCREF(r) Py_INCREF(r)
+  #define __Pyx_DECREF(r) Py_DECREF(r)
+  #define __Pyx_GOTREF(r)
+  #define __Pyx_GIVEREF(r)
+  #define __Pyx_XINCREF(r) Py_XINCREF(r)
+  #define __Pyx_XDECREF(r) Py_XDECREF(r)
+  #define __Pyx_XGOTREF(r)
+  #define __Pyx_XGIVEREF(r)
+#endif
+#define __Pyx_Py_XDECREF_SET(r, v) do {\
+        PyObject *tmp = (PyObject *) r;\
+        r = v; Py_XDECREF(tmp);\
+    } while (0)
+#define __Pyx_XDECREF_SET(r, v) do {\
+        PyObject *tmp = (PyObject *) r;\
+        r = v; __Pyx_XDECREF(tmp);\
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+#define __Pyx_DECREF_SET(r, v) do {\
+        PyObject *tmp = (PyObject *) r;\
+        r = v; __Pyx_DECREF(tmp);\
+    } while (0)
+#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
+#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)
+
+/* PyErrExceptionMatches.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
+static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
+#else
+#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
+#endif
+
+/* PyThreadStateGet.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
+#define __Pyx_PyThreadState_assign  __pyx_tstate = __Pyx_PyThreadState_Current;
+#if PY_VERSION_HEX >= 0x030C00A6
+#define __Pyx_PyErr_Occurred()  (__pyx_tstate->current_exception != NULL)
+#define __Pyx_PyErr_CurrentExceptionType()  (__pyx_tstate->current_exception ? (PyObject*) Py_TYPE(__pyx_tstate->current_exception) : (PyObject*) NULL)
+#else
+#define __Pyx_PyErr_Occurred()  (__pyx_tstate->curexc_type != NULL)
+#define __Pyx_PyErr_CurrentExceptionType()  (__pyx_tstate->curexc_type)
+#endif
+#else
+#define __Pyx_PyThreadState_declare
+#define __Pyx_PyThreadState_assign
+#define __Pyx_PyErr_Occurred()  (PyErr_Occurred() != NULL)
+#define __Pyx_PyErr_CurrentExceptionType()  PyErr_Occurred()
+#endif
+
+/* PyErrFetchRestore.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
+#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
+#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
+#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
+#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
+static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A6
+#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
+#else
+#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
+#endif
+#else
+#define __Pyx_PyErr_Clear() PyErr_Clear()
+#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
+#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
+#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
+#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
+#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
+#endif
+
+/* PyObjectGetAttrStr.proto */
+#if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
+#else
+#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
+#endif
+
+/* PyObjectGetAttrStrNoError.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name);
+
+/* GetBuiltinName.proto */
+static PyObject *__Pyx_GetBuiltinName(PyObject *name);
+
+/* GetTopmostException.proto */
+#if CYTHON_USE_EXC_INFO_STACK && CYTHON_FAST_THREAD_STATE
+static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
+#endif
+
+/* SaveResetException.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
+static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
+#else
+#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
+#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
+#endif
+
+/* GetException.proto */
+#if CYTHON_FAST_THREAD_STATE
+#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
+static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
+#else
+static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
+#endif
+
+/* PyObjectCall.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
+#else
+#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
+#endif
+
+/* RaiseException.proto */
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);
+
+/* IsLittleEndian.proto */
+static CYTHON_INLINE int __Pyx_Is_Little_Endian(void);
+
+/* BufferFormatCheck.proto */
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts);
+static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
+                              __Pyx_BufFmt_StackElem* stack,
+                              __Pyx_TypeInfo* type);
+
+/* BufferGetAndValidate.proto */
+#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\
+    ((obj == Py_None || obj == NULL) ?\
+    (__Pyx_ZeroBuffer(buf), 0) :\
+    __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack))
+static int  __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
+    __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
+static void __Pyx_ZeroBuffer(Py_buffer* buf);
+static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
+static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 };
+static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 };
+
+/* BufferIndexError.proto */
+static void __Pyx_RaiseBufferIndexError(int axis);
+
+#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
+/* TupleAndListFromArray.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n);
+static CYTHON_INLINE PyObject* __Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n);
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+
+/* IncludeStringH.proto */
+#include <string.h>
+
+/* BytesEquals.proto */
+static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
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+/* UnicodeEquals.proto */
+static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
+
+/* fastcall.proto */
+#if CYTHON_AVOID_BORROWED_REFS
+    #define __Pyx_Arg_VARARGS(args, i) PySequence_GetItem(args, i)
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+    #define __Pyx_Arg_VARARGS(args, i) PyTuple_GET_ITEM(args, i)
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+    #define __Pyx_Arg_VARARGS(args, i) PyTuple_GetItem(args, i)
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+#if CYTHON_AVOID_BORROWED_REFS
+    #define __Pyx_Arg_NewRef_VARARGS(arg) __Pyx_NewRef(arg)
+    #define __Pyx_Arg_XDECREF_VARARGS(arg) Py_XDECREF(arg)
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+    #define __Pyx_Arg_NewRef_VARARGS(arg) arg
+    #define __Pyx_Arg_XDECREF_VARARGS(arg)
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+#define __Pyx_NumKwargs_VARARGS(kwds) PyDict_Size(kwds)
+#define __Pyx_KwValues_VARARGS(args, nargs) NULL
+#define __Pyx_GetKwValue_VARARGS(kw, kwvalues, s) __Pyx_PyDict_GetItemStrWithError(kw, s)
+#define __Pyx_KwargsAsDict_VARARGS(kw, kwvalues) PyDict_Copy(kw)
+#if CYTHON_METH_FASTCALL
+    #define __Pyx_Arg_FASTCALL(args, i) args[i]
+    #define __Pyx_NumKwargs_FASTCALL(kwds) PyTuple_GET_SIZE(kwds)
+    #define __Pyx_KwValues_FASTCALL(args, nargs) ((args) + (nargs))
+    static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s);
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000
+    CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues);
+  #else
+    #define __Pyx_KwargsAsDict_FASTCALL(kw, kwvalues) _PyStack_AsDict(kwvalues, kw)
+  #endif
+    #define __Pyx_Arg_NewRef_FASTCALL(arg) arg  /* no-op, __Pyx_Arg_FASTCALL is direct and this needs
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+    #define __Pyx_Arg_XDECREF_FASTCALL(arg)
+#else
+    #define __Pyx_Arg_FASTCALL __Pyx_Arg_VARARGS
+    #define __Pyx_NumKwargs_FASTCALL __Pyx_NumKwargs_VARARGS
+    #define __Pyx_KwValues_FASTCALL __Pyx_KwValues_VARARGS
+    #define __Pyx_GetKwValue_FASTCALL __Pyx_GetKwValue_VARARGS
+    #define __Pyx_KwargsAsDict_FASTCALL __Pyx_KwargsAsDict_VARARGS
+    #define __Pyx_Arg_NewRef_FASTCALL(arg) __Pyx_Arg_NewRef_VARARGS(arg)
+    #define __Pyx_Arg_XDECREF_FASTCALL(arg) __Pyx_Arg_XDECREF_VARARGS(arg)
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+#define __Pyx_ArgsSlice_VARARGS(args, start, stop) __Pyx_PyTuple_FromArray(&__Pyx_Arg_VARARGS(args, start), stop - start)
+#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) __Pyx_PyTuple_FromArray(&__Pyx_Arg_FASTCALL(args, start), stop - start)
+#else
+#define __Pyx_ArgsSlice_VARARGS(args, start, stop) PyTuple_GetSlice(args, start, stop)
+#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) PyTuple_GetSlice(args, start, stop)
+#endif
+
+/* RaiseArgTupleInvalid.proto */
+static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
+    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);
+
+/* RaiseDoubleKeywords.proto */
+static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);
+
+/* ParseKeywords.proto */
+static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject *const *kwvalues,
+    PyObject **argnames[],
+    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,
+    const char* function_name);
+
+/* ArgTypeTest.proto */
+#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
+    ((likely(__Pyx_IS_TYPE(obj, type) | (none_allowed && (obj == Py_None)))) ? 1 :\
+        __Pyx__ArgTypeTest(obj, type, name, exact))
+static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
+
+#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1)
+/* TypeImport.proto */
+#ifndef __PYX_HAVE_RT_ImportType_proto_3_0_11
+#define __PYX_HAVE_RT_ImportType_proto_3_0_11
+#if defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L
+#include <stdalign.h>
+#endif
+#if (defined (__STDC_VERSION__) && __STDC_VERSION__ >= 201112L) || __cplusplus >= 201103L
+#define __PYX_GET_STRUCT_ALIGNMENT_3_0_11(s) alignof(s)
+#else
+#define __PYX_GET_STRUCT_ALIGNMENT_3_0_11(s) sizeof(void*)
+#endif
+enum __Pyx_ImportType_CheckSize_3_0_11 {
+   __Pyx_ImportType_CheckSize_Error_3_0_11 = 0,
+   __Pyx_ImportType_CheckSize_Warn_3_0_11 = 1,
+   __Pyx_ImportType_CheckSize_Ignore_3_0_11 = 2
+};
+static PyTypeObject *__Pyx_ImportType_3_0_11(PyObject* module, const char *module_name, const char *class_name, size_t size, size_t alignment, enum __Pyx_ImportType_CheckSize_3_0_11 check_size);
+#endif
+
+/* Import.proto */
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
+
+/* ImportDottedModule.proto */
+static PyObject *__Pyx_ImportDottedModule(PyObject *name, PyObject *parts_tuple);
+#if PY_MAJOR_VERSION >= 3
+static PyObject *__Pyx_ImportDottedModule_WalkParts(PyObject *module, PyObject *name, PyObject *parts_tuple);
+#endif
+
+/* IncludeStructmemberH.proto */
+#include <structmember.h>
+
+/* FixUpExtensionType.proto */
+#if CYTHON_USE_TYPE_SPECS
+static int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type);
+#endif
+
+/* FetchSharedCythonModule.proto */
+static PyObject *__Pyx_FetchSharedCythonABIModule(void);
+
+/* FetchCommonType.proto */
+#if !CYTHON_USE_TYPE_SPECS
+static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);
+#else
+static PyTypeObject* __Pyx_FetchCommonTypeFromSpec(PyObject *module, PyType_Spec *spec, PyObject *bases);
+#endif
+
+/* PyMethodNew.proto */
+#if CYTHON_COMPILING_IN_LIMITED_API
+static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) {
+    PyObject *typesModule=NULL, *methodType=NULL, *result=NULL;
+    CYTHON_UNUSED_VAR(typ);
+    if (!self)
+        return __Pyx_NewRef(func);
+    typesModule = PyImport_ImportModule("types");
+    if (!typesModule) return NULL;
+    methodType = PyObject_GetAttrString(typesModule, "MethodType");
+    Py_DECREF(typesModule);
+    if (!methodType) return NULL;
+    result = PyObject_CallFunctionObjArgs(methodType, func, self, NULL);
+    Py_DECREF(methodType);
+    return result;
+}
+#elif PY_MAJOR_VERSION >= 3
+static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) {
+    CYTHON_UNUSED_VAR(typ);
+    if (!self)
+        return __Pyx_NewRef(func);
+    return PyMethod_New(func, self);
+}
+#else
+    #define __Pyx_PyMethod_New PyMethod_New
+#endif
+
+/* PyVectorcallFastCallDict.proto */
+#if CYTHON_METH_FASTCALL
+static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw);
+#endif
+
+/* CythonFunctionShared.proto */
+#define __Pyx_CyFunction_USED
+#define __Pyx_CYFUNCTION_STATICMETHOD  0x01
+#define __Pyx_CYFUNCTION_CLASSMETHOD   0x02
+#define __Pyx_CYFUNCTION_CCLASS        0x04
+#define __Pyx_CYFUNCTION_COROUTINE     0x08
+#define __Pyx_CyFunction_GetClosure(f)\
+    (((__pyx_CyFunctionObject *) (f))->func_closure)
+#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
+  #define __Pyx_CyFunction_GetClassObj(f)\
+      (((__pyx_CyFunctionObject *) (f))->func_classobj)
+#else
+  #define __Pyx_CyFunction_GetClassObj(f)\
+      ((PyObject*) ((PyCMethodObject *) (f))->mm_class)
+#endif
+#define __Pyx_CyFunction_SetClassObj(f, classobj)\
+    __Pyx__CyFunction_SetClassObj((__pyx_CyFunctionObject *) (f), (classobj))
+#define __Pyx_CyFunction_Defaults(type, f)\
+    ((type *)(((__pyx_CyFunctionObject *) (f))->defaults))
+#define __Pyx_CyFunction_SetDefaultsGetter(f, g)\
+    ((__pyx_CyFunctionObject *) (f))->defaults_getter = (g)
+typedef struct {
+#if CYTHON_COMPILING_IN_LIMITED_API
+    PyObject_HEAD
+    PyObject *func;
+#elif PY_VERSION_HEX < 0x030900B1
+    PyCFunctionObject func;
+#else
+    PyCMethodObject func;
+#endif
+#if CYTHON_BACKPORT_VECTORCALL
+    __pyx_vectorcallfunc func_vectorcall;
+#endif
+#if PY_VERSION_HEX < 0x030500A0 || CYTHON_COMPILING_IN_LIMITED_API
+    PyObject *func_weakreflist;
+#endif
+    PyObject *func_dict;
+    PyObject *func_name;
+    PyObject *func_qualname;
+    PyObject *func_doc;
+    PyObject *func_globals;
+    PyObject *func_code;
+    PyObject *func_closure;
+#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
+    PyObject *func_classobj;
+#endif
+    void *defaults;
+    int defaults_pyobjects;
+    size_t defaults_size;
+    int flags;
+    PyObject *defaults_tuple;
+    PyObject *defaults_kwdict;
+    PyObject *(*defaults_getter)(PyObject *);
+    PyObject *func_annotations;
+    PyObject *func_is_coroutine;
+} __pyx_CyFunctionObject;
+#undef __Pyx_CyOrPyCFunction_Check
+#define __Pyx_CyFunction_Check(obj)  __Pyx_TypeCheck(obj, __pyx_CyFunctionType)
+#define __Pyx_CyOrPyCFunction_Check(obj)  __Pyx_TypeCheck2(obj, __pyx_CyFunctionType, &PyCFunction_Type)
+#define __Pyx_CyFunction_CheckExact(obj)  __Pyx_IS_TYPE(obj, __pyx_CyFunctionType)
+static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void *cfunc);
+#undef __Pyx_IsSameCFunction
+#define __Pyx_IsSameCFunction(func, cfunc)   __Pyx__IsSameCyOrCFunction(func, cfunc)
+static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject* op, PyMethodDef *ml,
+                                      int flags, PyObject* qualname,
+                                      PyObject *closure,
+                                      PyObject *module, PyObject *globals,
+                                      PyObject* code);
+static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj);
+static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *m,
+                                                         size_t size,
+                                                         int pyobjects);
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *m,
+                                                            PyObject *tuple);
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *m,
+                                                             PyObject *dict);
+static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *m,
+                                                              PyObject *dict);
+static int __pyx_CyFunction_init(PyObject *module);
+#if CYTHON_METH_FASTCALL
+static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
+static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
+static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
+static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
+#if CYTHON_BACKPORT_VECTORCALL
+#define __Pyx_CyFunction_func_vectorcall(f) (((__pyx_CyFunctionObject*)f)->func_vectorcall)
+#else
+#define __Pyx_CyFunction_func_vectorcall(f) (((PyCFunctionObject*)f)->vectorcall)
+#endif
+#endif
+
+/* CythonFunction.proto */
+static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml,
+                                      int flags, PyObject* qualname,
+                                      PyObject *closure,
+                                      PyObject *module, PyObject *globals,
+                                      PyObject* code);
+
+/* PyDictVersioning.proto */
+#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
+#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
+#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
+    (version_var) = __PYX_GET_DICT_VERSION(dict);\
+    (cache_var) = (value);
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
+    static PY_UINT64_T __pyx_dict_version = 0;\
+    static PyObject *__pyx_dict_cached_value = NULL;\
+    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
+        (VAR) = __pyx_dict_cached_value;\
+    } else {\
+        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
+        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
+    }\
+}
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
+static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
+#else
+#define __PYX_GET_DICT_VERSION(dict)  (0)
+#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
+#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
+#endif
+
+/* CLineInTraceback.proto */
+#ifdef CYTHON_CLINE_IN_TRACEBACK
+#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
+#else
+static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
+#endif
+
+/* CodeObjectCache.proto */
+#if !CYTHON_COMPILING_IN_LIMITED_API
+typedef struct {
+    PyCodeObject* code_object;
+    int code_line;
+} __Pyx_CodeObjectCacheEntry;
+struct __Pyx_CodeObjectCache {
+    int count;
+    int max_count;
+    __Pyx_CodeObjectCacheEntry* entries;
+};
+static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
+static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
+static PyCodeObject *__pyx_find_code_object(int code_line);
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
+#endif
+
+/* AddTraceback.proto */
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename);
+
+/* BufferStructDeclare.proto */
+typedef struct {
+  Py_ssize_t shape, strides, suboffsets;
+} __Pyx_Buf_DimInfo;
+typedef struct {
+  size_t refcount;
+  Py_buffer pybuffer;
+} __Pyx_Buffer;
+typedef struct {
+  __Pyx_Buffer *rcbuffer;
+  char *data;
+  __Pyx_Buf_DimInfo diminfo[8];
+} __Pyx_LocalBuf_ND;
+
+#if PY_MAJOR_VERSION < 3
+    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
+    static void __Pyx_ReleaseBuffer(Py_buffer *view);
+#else
+    #define __Pyx_GetBuffer PyObject_GetBuffer
+    #define __Pyx_ReleaseBuffer PyBuffer_Release
+#endif
+
+
+/* GCCDiagnostics.proto */
+#if !defined(__INTEL_COMPILER) && defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
+#define __Pyx_HAS_GCC_DIAGNOSTIC
+#endif
+
+/* RealImag.proto */
+#if CYTHON_CCOMPLEX
+  #ifdef __cplusplus
+    #define __Pyx_CREAL(z) ((z).real())
+    #define __Pyx_CIMAG(z) ((z).imag())
+  #else
+    #define __Pyx_CREAL(z) (__real__(z))
+    #define __Pyx_CIMAG(z) (__imag__(z))
+  #endif
+#else
+    #define __Pyx_CREAL(z) ((z).real)
+    #define __Pyx_CIMAG(z) ((z).imag)
+#endif
+#if defined(__cplusplus) && CYTHON_CCOMPLEX\
+        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
+    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
+    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
+#else
+    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
+    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_float(a, b) ((a)-(b))
+    #define __Pyx_c_prod_float(a, b) ((a)*(b))
+    #define __Pyx_c_quot_float(a, b) ((a)/(b))
+    #define __Pyx_c_neg_float(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
+    #define __Pyx_c_conj_float(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_float(z)     (::std::abs(z))
+        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_float(z) ((z)==0)
+    #define __Pyx_c_conj_float(z)    (conjf(z))
+    #if 1
+        #define __Pyx_c_abs_float(z)     (cabsf(z))
+        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
+    #endif
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_double(a, b) ((a)-(b))
+    #define __Pyx_c_prod_double(a, b) ((a)*(b))
+    #define __Pyx_c_quot_double(a, b) ((a)/(b))
+    #define __Pyx_c_neg_double(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
+    #define __Pyx_c_conj_double(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_double(z)     (::std::abs(z))
+        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_double(z) ((z)==0)
+    #define __Pyx_c_conj_double(z)    (conj(z))
+    #if 1
+        #define __Pyx_c_abs_double(z)     (cabs(z))
+        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
+    #endif
+#endif
+
+/* Arithmetic.proto */
+#if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+    #define __Pyx_c_eq_long__double(a, b)   ((a)==(b))
+    #define __Pyx_c_sum_long__double(a, b)  ((a)+(b))
+    #define __Pyx_c_diff_long__double(a, b) ((a)-(b))
+    #define __Pyx_c_prod_long__double(a, b) ((a)*(b))
+    #define __Pyx_c_quot_long__double(a, b) ((a)/(b))
+    #define __Pyx_c_neg_long__double(a)     (-(a))
+  #ifdef __cplusplus
+    #define __Pyx_c_is_zero_long__double(z) ((z)==(long double)0)
+    #define __Pyx_c_conj_long__double(z)    (::std::conj(z))
+    #if 1
+        #define __Pyx_c_abs_long__double(z)     (::std::abs(z))
+        #define __Pyx_c_pow_long__double(a, b)  (::std::pow(a, b))
+    #endif
+  #else
+    #define __Pyx_c_is_zero_long__double(z) ((z)==0)
+    #define __Pyx_c_conj_long__double(z)    (conjl(z))
+    #if 1
+        #define __Pyx_c_abs_long__double(z)     (cabsl(z))
+        #define __Pyx_c_pow_long__double(a, b)  (cpowl(a, b))
+    #endif
+ #endif
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_sum_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_diff_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_prod_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_neg_long__double(__pyx_t_long_double_complex);
+    static CYTHON_INLINE int __Pyx_c_is_zero_long__double(__pyx_t_long_double_complex);
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_conj_long__double(__pyx_t_long_double_complex);
+    #if 1
+        static CYTHON_INLINE long double __Pyx_c_abs_long__double(__pyx_t_long_double_complex);
+        static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_pow_long__double(__pyx_t_long_double_complex, __pyx_t_long_double_complex);
+    #endif
+#endif
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE uint32_t __Pyx_PyInt_As_uint32_t(PyObject *);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE uint16_t __Pyx_PyInt_As_uint16_t(PyObject *);
+
+/* FormatTypeName.proto */
+#if CYTHON_COMPILING_IN_LIMITED_API
+typedef PyObject *__Pyx_TypeName;
+#define __Pyx_FMT_TYPENAME "%U"
+static __Pyx_TypeName __Pyx_PyType_GetName(PyTypeObject* tp);
+#define __Pyx_DECREF_TypeName(obj) Py_XDECREF(obj)
+#else
+typedef const char *__Pyx_TypeName;
+#define __Pyx_FMT_TYPENAME "%.200s"
+#define __Pyx_PyType_GetName(tp) ((tp)->tp_name)
+#define __Pyx_DECREF_TypeName(obj)
+#endif
+
+/* CIntToPy.proto */
+static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
+
+/* CIntFromPy.proto */
+static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
+
+/* FastTypeChecks.proto */
+#if CYTHON_COMPILING_IN_CPYTHON
+#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
+#define __Pyx_TypeCheck2(obj, type1, type2) __Pyx_IsAnySubtype2(Py_TYPE(obj), (PyTypeObject *)type1, (PyTypeObject *)type2)
+static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
+static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b);
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
+#else
+#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
+#define __Pyx_TypeCheck2(obj, type1, type2) (PyObject_TypeCheck(obj, (PyTypeObject *)type1) || PyObject_TypeCheck(obj, (PyTypeObject *)type2))
+#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
+#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
+#endif
+#define __Pyx_PyErr_ExceptionMatches2(err1, err2)  __Pyx_PyErr_GivenExceptionMatches2(__Pyx_PyErr_CurrentExceptionType(), err1, err2)
+#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
+
+/* CheckBinaryVersion.proto */
+static unsigned long __Pyx_get_runtime_version(void);
+static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer);
+
+/* InitStrings.proto */
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
+
+/* #### Code section: module_declarations ### */
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_8itemsize_itemsize(PyArray_Descr *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_9alignment_alignment(PyArray_Descr *__pyx_v_self); /* proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_6fields_fields(PyArray_Descr *__pyx_v_self); /* proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_5names_names(PyArray_Descr *__pyx_v_self); /* proto*/
+static CYTHON_INLINE PyArray_ArrayDescr *__pyx_f_5numpy_5dtype_8subarray_subarray(PyArray_Descr *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_uint64 __pyx_f_5numpy_5dtype_5flags_flags(PyArray_Descr *__pyx_v_self); /* proto*/
+static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_7numiter_numiter(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_4size_size(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_5index_index(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_2nd_nd(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp *__pyx_f_5numpy_9broadcast_10dimensions_dimensions(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE void **__pyx_f_5numpy_9broadcast_5iters_iters(PyArrayMultiIterObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_7ndarray_4base_base(PyArrayObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE PyArray_Descr *__pyx_f_5numpy_7ndarray_5descr_descr(PyArrayObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE int __pyx_f_5numpy_7ndarray_4ndim_ndim(PyArrayObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_5shape_shape(PyArrayObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_7strides_strides(PyArrayObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_7ndarray_4size_size(PyArrayObject *__pyx_v_self); /* proto*/
+static CYTHON_INLINE char *__pyx_f_5numpy_7ndarray_4data_data(PyArrayObject *__pyx_v_self); /* proto*/
+
+/* Module declarations from "libc.string" */
+
+/* Module declarations from "libc.stdio" */
+
+/* Module declarations from "__builtin__" */
+
+/* Module declarations from "cpython.type" */
+
+/* Module declarations from "cpython" */
+
+/* Module declarations from "cpython.object" */
+
+/* Module declarations from "cpython.ref" */
+
+/* Module declarations from "numpy" */
+
+/* Module declarations from "numpy" */
+static CYTHON_INLINE int __pyx_f_5numpy_import_array(void); /*proto*/
+
+/* Module declarations from "libcpp" */
+
+/* Module declarations from "onlinemid.onlinemid.runningstats" */
+static PyObject *__pyx_f_9onlinemid_9onlinemid_12runningstats_compute_stats(PyArrayObject *, PyArrayObject *, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
+static PyObject *__pyx_f_9onlinemid_9onlinemid_12runningstats_compute_stats_simd(PyArrayObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *, uint32_t, int __pyx_skip_dispatch); /*proto*/
+static PyObject *__pyx_f_9onlinemid_9onlinemid_12runningstats_compute_stats_simd_float(PyArrayObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *, PyArrayObject *, uint32_t, int __pyx_skip_dispatch); /*proto*/
+static PyObject *__pyx_f_9onlinemid_9onlinemid_12runningstats_call_roi_stats(PyArrayObject *, uint32_t, uint32_t, PyArrayObject *, uint32_t, uint32_t, PyArrayObject *, uint16_t, PyArrayObject *, PyArrayObject *, int __pyx_skip_dispatch); /*proto*/
+/* #### Code section: typeinfo ### */
+static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t = { "float32_t", NULL, sizeof(__pyx_t_5numpy_float32_t), { 0 }, 0, 'R', 0, 0 };
+static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float64_t = { "float64_t", NULL, sizeof(__pyx_t_5numpy_float64_t), { 0 }, 0, 'R', 0, 0 };
+static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_uint32_t = { "uint32_t", NULL, sizeof(__pyx_t_5numpy_uint32_t), { 0 }, 0, __PYX_IS_UNSIGNED(__pyx_t_5numpy_uint32_t) ? 'U' : 'I', __PYX_IS_UNSIGNED(__pyx_t_5numpy_uint32_t), 0 };
+static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_int16_t = { "int16_t", NULL, sizeof(__pyx_t_5numpy_int16_t), { 0 }, 0, __PYX_IS_UNSIGNED(__pyx_t_5numpy_int16_t) ? 'U' : 'I', __PYX_IS_UNSIGNED(__pyx_t_5numpy_int16_t), 0 };
+/* #### Code section: before_global_var ### */
+#define __Pyx_MODULE_NAME "onlinemid.onlinemid.runningstats"
+extern int __pyx_module_is_main_onlinemid__onlinemid__runningstats;
+int __pyx_module_is_main_onlinemid__onlinemid__runningstats = 0;
+
+/* Implementation of "onlinemid.onlinemid.runningstats" */
+/* #### Code section: global_var ### */
+static PyObject *__pyx_builtin_ImportError;
+/* #### Code section: string_decls ### */
+static const char __pyx_k__3[] = "*";
+static const char __pyx_k_np[] = "np";
+static const char __pyx_k__11[] = "?";
+static const char __pyx_k_data[] = "data";
+static const char __pyx_k_main[] = "__main__";
+static const char __pyx_k_name[] = "__name__";
+static const char __pyx_k_spec[] = "__spec__";
+static const char __pyx_k_test[] = "__test__";
+static const char __pyx_k_numpy[] = "numpy";
+static const char __pyx_k_import[] = "__import__";
+static const char __pyx_k_num_rois[] = "num_rois";
+static const char __pyx_k_litframes[] = "litframes";
+static const char __pyx_k_image_size[] = "image_size";
+static const char __pyx_k_num_images[] = "num_images";
+static const char __pyx_k_online_roi[] = "online_roi";
+static const char __pyx_k_ImportError[] = "ImportError";
+static const char __pyx_k_num_threads[] = "num_threads";
+static const char __pyx_k_simd_offset[] = "simd_offset";
+static const char __pyx_k_initializing[] = "_initializing";
+static const char __pyx_k_is_coroutine[] = "_is_coroutine";
+static const char __pyx_k_compute_stats[] = "compute_stats";
+static const char __pyx_k_num_litframes[] = "num_litframes";
+static const char __pyx_k_simd_vec_size[] = "simd_vec_size";
+static const char __pyx_k_call_roi_stats[] = "call_roi_stats";
+static const char __pyx_k_nanmean_of_data[] = "nanmean_of_data";
+static const char __pyx_k_running_mean_mem[] = "running_mean_mem";
+static const char __pyx_k_asyncio_coroutines[] = "asyncio.coroutines";
+static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
+static const char __pyx_k_compute_stats_simd[] = "compute_stats_simd";
+static const char __pyx_k_memory_for_pixel_stats[] = "memory_for_pixel_stats";
+static const char __pyx_k_compute_stats_simd_float[] = "compute_stats_simd_float";
+static const char __pyx_k_online_roi_length_per_roi[] = "online_roi_length_per_roi";
+static const char __pyx_k_memory_for_bunch_resolved_roi_st[] = "memory_for_bunch_resolved_roi_stats";
+static const char __pyx_k_numpy__core_multiarray_failed_to[] = "numpy._core.multiarray failed to import";
+static const char __pyx_k_numpy__core_umath_failed_to_impo[] = "numpy._core.umath failed to import";
+static const char __pyx_k_onlinemid_onlinemid_runningstats[] = "onlinemid.onlinemid.runningstats";
+static const char __pyx_k_src_onlinemid_runningstats_runni[] = "src/onlinemid/runningstats/runningstats.pyx";
+/* #### Code section: decls ### */
+static PyObject *__pyx_pf_9onlinemid_9onlinemid_12runningstats_compute_stats(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_data, PyArrayObject *__pyx_v_running_mean_mem, PyArrayObject *__pyx_v_nanmean_of_data); /* proto */
+static PyObject *__pyx_pf_9onlinemid_9onlinemid_12runningstats_2compute_stats_simd(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_data, PyArrayObject *__pyx_v_running_mean_mem, PyArrayObject *__pyx_v_nanmean_of_data, PyArrayObject *__pyx_v_simd_vec_size, PyArrayObject *__pyx_v_simd_offset, uint32_t __pyx_v_num_threads); /* proto */
+static PyObject *__pyx_pf_9onlinemid_9onlinemid_12runningstats_4compute_stats_simd_float(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_data, PyArrayObject *__pyx_v_running_mean_mem, PyArrayObject *__pyx_v_nanmean_of_data, PyArrayObject *__pyx_v_simd_vec_size, PyArrayObject *__pyx_v_simd_offset, uint32_t __pyx_v_num_threads); /* proto */
+static PyObject *__pyx_pf_9onlinemid_9onlinemid_12runningstats_6call_roi_stats(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_data, uint32_t __pyx_v_image_size, uint32_t __pyx_v_num_images, PyArrayObject *__pyx_v_online_roi, uint32_t __pyx_v_num_rois, uint32_t __pyx_v_online_roi_length_per_roi, PyArrayObject *__pyx_v_litframes, uint16_t __pyx_v_num_litframes, PyArrayObject *__pyx_v_memory_for_bunch_resolved_roi_stats, PyArrayObject *__pyx_v_memory_for_pixel_stats); /* proto */
+/* #### Code section: late_includes ### */
+/* #### Code section: module_state ### */
+typedef struct {
+  PyObject *__pyx_d;
+  PyObject *__pyx_b;
+  PyObject *__pyx_cython_runtime;
+  PyObject *__pyx_empty_tuple;
+  PyObject *__pyx_empty_bytes;
+  PyObject *__pyx_empty_unicode;
+  #ifdef __Pyx_CyFunction_USED
+  PyTypeObject *__pyx_CyFunctionType;
+  #endif
+  #ifdef __Pyx_FusedFunction_USED
+  PyTypeObject *__pyx_FusedFunctionType;
+  #endif
+  #ifdef __Pyx_Generator_USED
+  PyTypeObject *__pyx_GeneratorType;
+  #endif
+  #ifdef __Pyx_IterableCoroutine_USED
+  PyTypeObject *__pyx_IterableCoroutineType;
+  #endif
+  #ifdef __Pyx_Coroutine_USED
+  PyTypeObject *__pyx_CoroutineAwaitType;
+  #endif
+  #ifdef __Pyx_Coroutine_USED
+  PyTypeObject *__pyx_CoroutineType;
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  PyTypeObject *__pyx_ptype_7cpython_4type_type;
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  PyTypeObject *__pyx_ptype_5numpy_dtype;
+  PyTypeObject *__pyx_ptype_5numpy_flatiter;
+  PyTypeObject *__pyx_ptype_5numpy_broadcast;
+  PyTypeObject *__pyx_ptype_5numpy_ndarray;
+  PyTypeObject *__pyx_ptype_5numpy_generic;
+  PyTypeObject *__pyx_ptype_5numpy_number;
+  PyTypeObject *__pyx_ptype_5numpy_integer;
+  PyTypeObject *__pyx_ptype_5numpy_signedinteger;
+  PyTypeObject *__pyx_ptype_5numpy_unsignedinteger;
+  PyTypeObject *__pyx_ptype_5numpy_inexact;
+  PyTypeObject *__pyx_ptype_5numpy_floating;
+  PyTypeObject *__pyx_ptype_5numpy_complexfloating;
+  PyTypeObject *__pyx_ptype_5numpy_flexible;
+  PyTypeObject *__pyx_ptype_5numpy_character;
+  PyTypeObject *__pyx_ptype_5numpy_ufunc;
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  #if CYTHON_USE_MODULE_STATE
+  #endif
+  PyObject *__pyx_n_s_ImportError;
+  PyObject *__pyx_n_s__11;
+  PyObject *__pyx_n_s__3;
+  PyObject *__pyx_n_s_asyncio_coroutines;
+  PyObject *__pyx_n_s_call_roi_stats;
+  PyObject *__pyx_n_s_cline_in_traceback;
+  PyObject *__pyx_n_s_compute_stats;
+  PyObject *__pyx_n_s_compute_stats_simd;
+  PyObject *__pyx_n_s_compute_stats_simd_float;
+  PyObject *__pyx_n_s_data;
+  PyObject *__pyx_n_s_image_size;
+  PyObject *__pyx_n_s_import;
+  PyObject *__pyx_n_s_initializing;
+  PyObject *__pyx_n_s_is_coroutine;
+  PyObject *__pyx_n_s_litframes;
+  PyObject *__pyx_n_s_main;
+  PyObject *__pyx_n_s_memory_for_bunch_resolved_roi_st;
+  PyObject *__pyx_n_s_memory_for_pixel_stats;
+  PyObject *__pyx_n_s_name;
+  PyObject *__pyx_n_s_nanmean_of_data;
+  PyObject *__pyx_n_s_np;
+  PyObject *__pyx_n_s_num_images;
+  PyObject *__pyx_n_s_num_litframes;
+  PyObject *__pyx_n_s_num_rois;
+  PyObject *__pyx_n_s_num_threads;
+  PyObject *__pyx_n_s_numpy;
+  PyObject *__pyx_kp_u_numpy__core_multiarray_failed_to;
+  PyObject *__pyx_kp_u_numpy__core_umath_failed_to_impo;
+  PyObject *__pyx_n_s_online_roi;
+  PyObject *__pyx_n_s_online_roi_length_per_roi;
+  PyObject *__pyx_n_s_onlinemid_onlinemid_runningstats;
+  PyObject *__pyx_n_s_running_mean_mem;
+  PyObject *__pyx_n_s_simd_offset;
+  PyObject *__pyx_n_s_simd_vec_size;
+  PyObject *__pyx_n_s_spec;
+  PyObject *__pyx_kp_s_src_onlinemid_runningstats_runni;
+  PyObject *__pyx_n_s_test;
+  PyObject *__pyx_tuple_;
+  PyObject *__pyx_tuple__2;
+  PyObject *__pyx_tuple__4;
+  PyObject *__pyx_tuple__6;
+  PyObject *__pyx_tuple__9;
+  PyObject *__pyx_codeobj__5;
+  PyObject *__pyx_codeobj__7;
+  PyObject *__pyx_codeobj__8;
+  PyObject *__pyx_codeobj__10;
+} __pyx_mstate;
+
+#if CYTHON_USE_MODULE_STATE
+#ifdef __cplusplus
+namespace {
+  extern struct PyModuleDef __pyx_moduledef;
+} /* anonymous namespace */
+#else
+static struct PyModuleDef __pyx_moduledef;
+#endif
+
+#define __pyx_mstate(o) ((__pyx_mstate *)__Pyx_PyModule_GetState(o))
+
+#define __pyx_mstate_global (__pyx_mstate(PyState_FindModule(&__pyx_moduledef)))
+
+#define __pyx_m (PyState_FindModule(&__pyx_moduledef))
+#else
+static __pyx_mstate __pyx_mstate_global_static =
+#ifdef __cplusplus
+    {};
+#else
+    {0};
+#endif
+static __pyx_mstate *__pyx_mstate_global = &__pyx_mstate_global_static;
+#endif
+/* #### Code section: module_state_clear ### */
+#if CYTHON_USE_MODULE_STATE
+static int __pyx_m_clear(PyObject *m) {
+  __pyx_mstate *clear_module_state = __pyx_mstate(m);
+  if (!clear_module_state) return 0;
+  Py_CLEAR(clear_module_state->__pyx_d);
+  Py_CLEAR(clear_module_state->__pyx_b);
+  Py_CLEAR(clear_module_state->__pyx_cython_runtime);
+  Py_CLEAR(clear_module_state->__pyx_empty_tuple);
+  Py_CLEAR(clear_module_state->__pyx_empty_bytes);
+  Py_CLEAR(clear_module_state->__pyx_empty_unicode);
+  #ifdef __Pyx_CyFunction_USED
+  Py_CLEAR(clear_module_state->__pyx_CyFunctionType);
+  #endif
+  #ifdef __Pyx_FusedFunction_USED
+  Py_CLEAR(clear_module_state->__pyx_FusedFunctionType);
+  #endif
+  Py_CLEAR(clear_module_state->__pyx_ptype_7cpython_4type_type);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_dtype);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_flatiter);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_broadcast);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_ndarray);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_generic);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_number);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_integer);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_signedinteger);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_unsignedinteger);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_inexact);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_floating);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_complexfloating);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_flexible);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_character);
+  Py_CLEAR(clear_module_state->__pyx_ptype_5numpy_ufunc);
+  Py_CLEAR(clear_module_state->__pyx_n_s_ImportError);
+  Py_CLEAR(clear_module_state->__pyx_n_s__11);
+  Py_CLEAR(clear_module_state->__pyx_n_s__3);
+  Py_CLEAR(clear_module_state->__pyx_n_s_asyncio_coroutines);
+  Py_CLEAR(clear_module_state->__pyx_n_s_call_roi_stats);
+  Py_CLEAR(clear_module_state->__pyx_n_s_cline_in_traceback);
+  Py_CLEAR(clear_module_state->__pyx_n_s_compute_stats);
+  Py_CLEAR(clear_module_state->__pyx_n_s_compute_stats_simd);
+  Py_CLEAR(clear_module_state->__pyx_n_s_compute_stats_simd_float);
+  Py_CLEAR(clear_module_state->__pyx_n_s_data);
+  Py_CLEAR(clear_module_state->__pyx_n_s_image_size);
+  Py_CLEAR(clear_module_state->__pyx_n_s_import);
+  Py_CLEAR(clear_module_state->__pyx_n_s_initializing);
+  Py_CLEAR(clear_module_state->__pyx_n_s_is_coroutine);
+  Py_CLEAR(clear_module_state->__pyx_n_s_litframes);
+  Py_CLEAR(clear_module_state->__pyx_n_s_main);
+  Py_CLEAR(clear_module_state->__pyx_n_s_memory_for_bunch_resolved_roi_st);
+  Py_CLEAR(clear_module_state->__pyx_n_s_memory_for_pixel_stats);
+  Py_CLEAR(clear_module_state->__pyx_n_s_name);
+  Py_CLEAR(clear_module_state->__pyx_n_s_nanmean_of_data);
+  Py_CLEAR(clear_module_state->__pyx_n_s_np);
+  Py_CLEAR(clear_module_state->__pyx_n_s_num_images);
+  Py_CLEAR(clear_module_state->__pyx_n_s_num_litframes);
+  Py_CLEAR(clear_module_state->__pyx_n_s_num_rois);
+  Py_CLEAR(clear_module_state->__pyx_n_s_num_threads);
+  Py_CLEAR(clear_module_state->__pyx_n_s_numpy);
+  Py_CLEAR(clear_module_state->__pyx_kp_u_numpy__core_multiarray_failed_to);
+  Py_CLEAR(clear_module_state->__pyx_kp_u_numpy__core_umath_failed_to_impo);
+  Py_CLEAR(clear_module_state->__pyx_n_s_online_roi);
+  Py_CLEAR(clear_module_state->__pyx_n_s_online_roi_length_per_roi);
+  Py_CLEAR(clear_module_state->__pyx_n_s_onlinemid_onlinemid_runningstats);
+  Py_CLEAR(clear_module_state->__pyx_n_s_running_mean_mem);
+  Py_CLEAR(clear_module_state->__pyx_n_s_simd_offset);
+  Py_CLEAR(clear_module_state->__pyx_n_s_simd_vec_size);
+  Py_CLEAR(clear_module_state->__pyx_n_s_spec);
+  Py_CLEAR(clear_module_state->__pyx_kp_s_src_onlinemid_runningstats_runni);
+  Py_CLEAR(clear_module_state->__pyx_n_s_test);
+  Py_CLEAR(clear_module_state->__pyx_tuple_);
+  Py_CLEAR(clear_module_state->__pyx_tuple__2);
+  Py_CLEAR(clear_module_state->__pyx_tuple__4);
+  Py_CLEAR(clear_module_state->__pyx_tuple__6);
+  Py_CLEAR(clear_module_state->__pyx_tuple__9);
+  Py_CLEAR(clear_module_state->__pyx_codeobj__5);
+  Py_CLEAR(clear_module_state->__pyx_codeobj__7);
+  Py_CLEAR(clear_module_state->__pyx_codeobj__8);
+  Py_CLEAR(clear_module_state->__pyx_codeobj__10);
+  return 0;
+}
+#endif
+/* #### Code section: module_state_traverse ### */
+#if CYTHON_USE_MODULE_STATE
+static int __pyx_m_traverse(PyObject *m, visitproc visit, void *arg) {
+  __pyx_mstate *traverse_module_state = __pyx_mstate(m);
+  if (!traverse_module_state) return 0;
+  Py_VISIT(traverse_module_state->__pyx_d);
+  Py_VISIT(traverse_module_state->__pyx_b);
+  Py_VISIT(traverse_module_state->__pyx_cython_runtime);
+  Py_VISIT(traverse_module_state->__pyx_empty_tuple);
+  Py_VISIT(traverse_module_state->__pyx_empty_bytes);
+  Py_VISIT(traverse_module_state->__pyx_empty_unicode);
+  #ifdef __Pyx_CyFunction_USED
+  Py_VISIT(traverse_module_state->__pyx_CyFunctionType);
+  #endif
+  #ifdef __Pyx_FusedFunction_USED
+  Py_VISIT(traverse_module_state->__pyx_FusedFunctionType);
+  #endif
+  Py_VISIT(traverse_module_state->__pyx_ptype_7cpython_4type_type);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_dtype);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_flatiter);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_broadcast);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_ndarray);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_generic);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_number);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_integer);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_signedinteger);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_unsignedinteger);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_inexact);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_floating);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_complexfloating);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_flexible);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_character);
+  Py_VISIT(traverse_module_state->__pyx_ptype_5numpy_ufunc);
+  Py_VISIT(traverse_module_state->__pyx_n_s_ImportError);
+  Py_VISIT(traverse_module_state->__pyx_n_s__11);
+  Py_VISIT(traverse_module_state->__pyx_n_s__3);
+  Py_VISIT(traverse_module_state->__pyx_n_s_asyncio_coroutines);
+  Py_VISIT(traverse_module_state->__pyx_n_s_call_roi_stats);
+  Py_VISIT(traverse_module_state->__pyx_n_s_cline_in_traceback);
+  Py_VISIT(traverse_module_state->__pyx_n_s_compute_stats);
+  Py_VISIT(traverse_module_state->__pyx_n_s_compute_stats_simd);
+  Py_VISIT(traverse_module_state->__pyx_n_s_compute_stats_simd_float);
+  Py_VISIT(traverse_module_state->__pyx_n_s_data);
+  Py_VISIT(traverse_module_state->__pyx_n_s_image_size);
+  Py_VISIT(traverse_module_state->__pyx_n_s_import);
+  Py_VISIT(traverse_module_state->__pyx_n_s_initializing);
+  Py_VISIT(traverse_module_state->__pyx_n_s_is_coroutine);
+  Py_VISIT(traverse_module_state->__pyx_n_s_litframes);
+  Py_VISIT(traverse_module_state->__pyx_n_s_main);
+  Py_VISIT(traverse_module_state->__pyx_n_s_memory_for_bunch_resolved_roi_st);
+  Py_VISIT(traverse_module_state->__pyx_n_s_memory_for_pixel_stats);
+  Py_VISIT(traverse_module_state->__pyx_n_s_name);
+  Py_VISIT(traverse_module_state->__pyx_n_s_nanmean_of_data);
+  Py_VISIT(traverse_module_state->__pyx_n_s_np);
+  Py_VISIT(traverse_module_state->__pyx_n_s_num_images);
+  Py_VISIT(traverse_module_state->__pyx_n_s_num_litframes);
+  Py_VISIT(traverse_module_state->__pyx_n_s_num_rois);
+  Py_VISIT(traverse_module_state->__pyx_n_s_num_threads);
+  Py_VISIT(traverse_module_state->__pyx_n_s_numpy);
+  Py_VISIT(traverse_module_state->__pyx_kp_u_numpy__core_multiarray_failed_to);
+  Py_VISIT(traverse_module_state->__pyx_kp_u_numpy__core_umath_failed_to_impo);
+  Py_VISIT(traverse_module_state->__pyx_n_s_online_roi);
+  Py_VISIT(traverse_module_state->__pyx_n_s_online_roi_length_per_roi);
+  Py_VISIT(traverse_module_state->__pyx_n_s_onlinemid_onlinemid_runningstats);
+  Py_VISIT(traverse_module_state->__pyx_n_s_running_mean_mem);
+  Py_VISIT(traverse_module_state->__pyx_n_s_simd_offset);
+  Py_VISIT(traverse_module_state->__pyx_n_s_simd_vec_size);
+  Py_VISIT(traverse_module_state->__pyx_n_s_spec);
+  Py_VISIT(traverse_module_state->__pyx_kp_s_src_onlinemid_runningstats_runni);
+  Py_VISIT(traverse_module_state->__pyx_n_s_test);
+  Py_VISIT(traverse_module_state->__pyx_tuple_);
+  Py_VISIT(traverse_module_state->__pyx_tuple__2);
+  Py_VISIT(traverse_module_state->__pyx_tuple__4);
+  Py_VISIT(traverse_module_state->__pyx_tuple__6);
+  Py_VISIT(traverse_module_state->__pyx_tuple__9);
+  Py_VISIT(traverse_module_state->__pyx_codeobj__5);
+  Py_VISIT(traverse_module_state->__pyx_codeobj__7);
+  Py_VISIT(traverse_module_state->__pyx_codeobj__8);
+  Py_VISIT(traverse_module_state->__pyx_codeobj__10);
+  return 0;
+}
+#endif
+/* #### Code section: module_state_defines ### */
+#define __pyx_d __pyx_mstate_global->__pyx_d
+#define __pyx_b __pyx_mstate_global->__pyx_b
+#define __pyx_cython_runtime __pyx_mstate_global->__pyx_cython_runtime
+#define __pyx_empty_tuple __pyx_mstate_global->__pyx_empty_tuple
+#define __pyx_empty_bytes __pyx_mstate_global->__pyx_empty_bytes
+#define __pyx_empty_unicode __pyx_mstate_global->__pyx_empty_unicode
+#ifdef __Pyx_CyFunction_USED
+#define __pyx_CyFunctionType __pyx_mstate_global->__pyx_CyFunctionType
+#endif
+#ifdef __Pyx_FusedFunction_USED
+#define __pyx_FusedFunctionType __pyx_mstate_global->__pyx_FusedFunctionType
+#endif
+#ifdef __Pyx_Generator_USED
+#define __pyx_GeneratorType __pyx_mstate_global->__pyx_GeneratorType
+#endif
+#ifdef __Pyx_IterableCoroutine_USED
+#define __pyx_IterableCoroutineType __pyx_mstate_global->__pyx_IterableCoroutineType
+#endif
+#ifdef __Pyx_Coroutine_USED
+#define __pyx_CoroutineAwaitType __pyx_mstate_global->__pyx_CoroutineAwaitType
+#endif
+#ifdef __Pyx_Coroutine_USED
+#define __pyx_CoroutineType __pyx_mstate_global->__pyx_CoroutineType
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#define __pyx_ptype_7cpython_4type_type __pyx_mstate_global->__pyx_ptype_7cpython_4type_type
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#define __pyx_ptype_5numpy_dtype __pyx_mstate_global->__pyx_ptype_5numpy_dtype
+#define __pyx_ptype_5numpy_flatiter __pyx_mstate_global->__pyx_ptype_5numpy_flatiter
+#define __pyx_ptype_5numpy_broadcast __pyx_mstate_global->__pyx_ptype_5numpy_broadcast
+#define __pyx_ptype_5numpy_ndarray __pyx_mstate_global->__pyx_ptype_5numpy_ndarray
+#define __pyx_ptype_5numpy_generic __pyx_mstate_global->__pyx_ptype_5numpy_generic
+#define __pyx_ptype_5numpy_number __pyx_mstate_global->__pyx_ptype_5numpy_number
+#define __pyx_ptype_5numpy_integer __pyx_mstate_global->__pyx_ptype_5numpy_integer
+#define __pyx_ptype_5numpy_signedinteger __pyx_mstate_global->__pyx_ptype_5numpy_signedinteger
+#define __pyx_ptype_5numpy_unsignedinteger __pyx_mstate_global->__pyx_ptype_5numpy_unsignedinteger
+#define __pyx_ptype_5numpy_inexact __pyx_mstate_global->__pyx_ptype_5numpy_inexact
+#define __pyx_ptype_5numpy_floating __pyx_mstate_global->__pyx_ptype_5numpy_floating
+#define __pyx_ptype_5numpy_complexfloating __pyx_mstate_global->__pyx_ptype_5numpy_complexfloating
+#define __pyx_ptype_5numpy_flexible __pyx_mstate_global->__pyx_ptype_5numpy_flexible
+#define __pyx_ptype_5numpy_character __pyx_mstate_global->__pyx_ptype_5numpy_character
+#define __pyx_ptype_5numpy_ufunc __pyx_mstate_global->__pyx_ptype_5numpy_ufunc
+#if CYTHON_USE_MODULE_STATE
+#endif
+#if CYTHON_USE_MODULE_STATE
+#endif
+#define __pyx_n_s_ImportError __pyx_mstate_global->__pyx_n_s_ImportError
+#define __pyx_n_s__11 __pyx_mstate_global->__pyx_n_s__11
+#define __pyx_n_s__3 __pyx_mstate_global->__pyx_n_s__3
+#define __pyx_n_s_asyncio_coroutines __pyx_mstate_global->__pyx_n_s_asyncio_coroutines
+#define __pyx_n_s_call_roi_stats __pyx_mstate_global->__pyx_n_s_call_roi_stats
+#define __pyx_n_s_cline_in_traceback __pyx_mstate_global->__pyx_n_s_cline_in_traceback
+#define __pyx_n_s_compute_stats __pyx_mstate_global->__pyx_n_s_compute_stats
+#define __pyx_n_s_compute_stats_simd __pyx_mstate_global->__pyx_n_s_compute_stats_simd
+#define __pyx_n_s_compute_stats_simd_float __pyx_mstate_global->__pyx_n_s_compute_stats_simd_float
+#define __pyx_n_s_data __pyx_mstate_global->__pyx_n_s_data
+#define __pyx_n_s_image_size __pyx_mstate_global->__pyx_n_s_image_size
+#define __pyx_n_s_import __pyx_mstate_global->__pyx_n_s_import
+#define __pyx_n_s_initializing __pyx_mstate_global->__pyx_n_s_initializing
+#define __pyx_n_s_is_coroutine __pyx_mstate_global->__pyx_n_s_is_coroutine
+#define __pyx_n_s_litframes __pyx_mstate_global->__pyx_n_s_litframes
+#define __pyx_n_s_main __pyx_mstate_global->__pyx_n_s_main
+#define __pyx_n_s_memory_for_bunch_resolved_roi_st __pyx_mstate_global->__pyx_n_s_memory_for_bunch_resolved_roi_st
+#define __pyx_n_s_memory_for_pixel_stats __pyx_mstate_global->__pyx_n_s_memory_for_pixel_stats
+#define __pyx_n_s_name __pyx_mstate_global->__pyx_n_s_name
+#define __pyx_n_s_nanmean_of_data __pyx_mstate_global->__pyx_n_s_nanmean_of_data
+#define __pyx_n_s_np __pyx_mstate_global->__pyx_n_s_np
+#define __pyx_n_s_num_images __pyx_mstate_global->__pyx_n_s_num_images
+#define __pyx_n_s_num_litframes __pyx_mstate_global->__pyx_n_s_num_litframes
+#define __pyx_n_s_num_rois __pyx_mstate_global->__pyx_n_s_num_rois
+#define __pyx_n_s_num_threads __pyx_mstate_global->__pyx_n_s_num_threads
+#define __pyx_n_s_numpy __pyx_mstate_global->__pyx_n_s_numpy
+#define __pyx_kp_u_numpy__core_multiarray_failed_to __pyx_mstate_global->__pyx_kp_u_numpy__core_multiarray_failed_to
+#define __pyx_kp_u_numpy__core_umath_failed_to_impo __pyx_mstate_global->__pyx_kp_u_numpy__core_umath_failed_to_impo
+#define __pyx_n_s_online_roi __pyx_mstate_global->__pyx_n_s_online_roi
+#define __pyx_n_s_online_roi_length_per_roi __pyx_mstate_global->__pyx_n_s_online_roi_length_per_roi
+#define __pyx_n_s_onlinemid_onlinemid_runningstats __pyx_mstate_global->__pyx_n_s_onlinemid_onlinemid_runningstats
+#define __pyx_n_s_running_mean_mem __pyx_mstate_global->__pyx_n_s_running_mean_mem
+#define __pyx_n_s_simd_offset __pyx_mstate_global->__pyx_n_s_simd_offset
+#define __pyx_n_s_simd_vec_size __pyx_mstate_global->__pyx_n_s_simd_vec_size
+#define __pyx_n_s_spec __pyx_mstate_global->__pyx_n_s_spec
+#define __pyx_kp_s_src_onlinemid_runningstats_runni __pyx_mstate_global->__pyx_kp_s_src_onlinemid_runningstats_runni
+#define __pyx_n_s_test __pyx_mstate_global->__pyx_n_s_test
+#define __pyx_tuple_ __pyx_mstate_global->__pyx_tuple_
+#define __pyx_tuple__2 __pyx_mstate_global->__pyx_tuple__2
+#define __pyx_tuple__4 __pyx_mstate_global->__pyx_tuple__4
+#define __pyx_tuple__6 __pyx_mstate_global->__pyx_tuple__6
+#define __pyx_tuple__9 __pyx_mstate_global->__pyx_tuple__9
+#define __pyx_codeobj__5 __pyx_mstate_global->__pyx_codeobj__5
+#define __pyx_codeobj__7 __pyx_mstate_global->__pyx_codeobj__7
+#define __pyx_codeobj__8 __pyx_mstate_global->__pyx_codeobj__8
+#define __pyx_codeobj__10 __pyx_mstate_global->__pyx_codeobj__10
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+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":286
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+ *         @property
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+ */
+
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_8itemsize_itemsize(PyArray_Descr *__pyx_v_self) {
+  npy_intp __pyx_r;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":287
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+ *         cdef inline npy_intp itemsize(self) noexcept nogil:
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+ * 
+ *         @property
+ */
+  __pyx_r = PyDataType_ELSIZE(__pyx_v_self);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":286
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+ *         @property
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+ */
+
+  /* function exit code */
+  __pyx_L0:;
+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":290
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+ *         @property
+ *         cdef inline npy_intp alignment(self) noexcept nogil:             # <<<<<<<<<<<<<<
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+static CYTHON_INLINE npy_intp __pyx_f_5numpy_5dtype_9alignment_alignment(PyArray_Descr *__pyx_v_self) {
+  npy_intp __pyx_r;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":291
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+ *         # Use fields/names with care as they may be NULL.  You must check
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+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":290
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+  /* function exit code */
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+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":296
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+static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_6fields_fields(PyArray_Descr *__pyx_v_self) {
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+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":296
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+  /* function exit code */
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+static CYTHON_INLINE PyObject *__pyx_f_5numpy_5dtype_5names_names(PyArray_Descr *__pyx_v_self) {
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+ * 
+ *         # Use PyDataType_HASSUBARRAY to test whether this field is
+ */
+  __Pyx_XDECREF(__pyx_r);
+  __pyx_t_1 = PyDataType_NAMES(__pyx_v_self);
+  __Pyx_INCREF(((PyObject*)__pyx_t_1));
+  __pyx_r = ((PyObject*)__pyx_t_1);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":300
+ * 
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+  /* function exit code */
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+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":307
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+ */
+
+static CYTHON_INLINE PyArray_ArrayDescr *__pyx_f_5numpy_5dtype_8subarray_subarray(PyArray_Descr *__pyx_v_self) {
+  PyArray_ArrayDescr *__pyx_r;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":308
+ *         @property
+ *         cdef inline PyArray_ArrayDescr* subarray(self) noexcept nogil:
+ *             return PyDataType_SUBARRAY(self)             # <<<<<<<<<<<<<<
+ * 
+ *         @property
+ */
+  __pyx_r = PyDataType_SUBARRAY(__pyx_v_self);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":307
+ *         # this field via the inline helper method PyDataType_SHAPE.
+ *         @property
+ *         cdef inline PyArray_ArrayDescr* subarray(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             return PyDataType_SUBARRAY(self)
+ * 
+ */
+
+  /* function exit code */
+  __pyx_L0:;
+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":311
+ * 
+ *         @property
+ *         cdef inline npy_uint64 flags(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The data types flags."""
+ *             return PyDataType_FLAGS(self)
+ */
+
+static CYTHON_INLINE npy_uint64 __pyx_f_5numpy_5dtype_5flags_flags(PyArray_Descr *__pyx_v_self) {
+  npy_uint64 __pyx_r;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":313
+ *         cdef inline npy_uint64 flags(self) noexcept nogil:
+ *             """The data types flags."""
+ *             return PyDataType_FLAGS(self)             # <<<<<<<<<<<<<<
+ * 
+ * 
+ */
+  __pyx_r = PyDataType_FLAGS(__pyx_v_self);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":311
+ * 
+ *         @property
+ *         cdef inline npy_uint64 flags(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The data types flags."""
+ *             return PyDataType_FLAGS(self)
+ */
+
+  /* function exit code */
+  __pyx_L0:;
+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":323
+ * 
+ *         @property
+ *         cdef inline int numiter(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The number of arrays that need to be broadcast to the same shape."""
+ *             return PyArray_MultiIter_NUMITER(self)
+ */
+
+static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_7numiter_numiter(PyArrayMultiIterObject *__pyx_v_self) {
+  int __pyx_r;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":325
+ *         cdef inline int numiter(self) noexcept nogil:
+ *             """The number of arrays that need to be broadcast to the same shape."""
+ *             return PyArray_MultiIter_NUMITER(self)             # <<<<<<<<<<<<<<
+ * 
+ *         @property
+ */
+  __pyx_r = PyArray_MultiIter_NUMITER(__pyx_v_self);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":323
+ * 
+ *         @property
+ *         cdef inline int numiter(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The number of arrays that need to be broadcast to the same shape."""
+ *             return PyArray_MultiIter_NUMITER(self)
+ */
+
+  /* function exit code */
+  __pyx_L0:;
+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":328
+ * 
+ *         @property
+ *         cdef inline npy_intp size(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The total broadcasted size."""
+ *             return PyArray_MultiIter_SIZE(self)
+ */
+
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_4size_size(PyArrayMultiIterObject *__pyx_v_self) {
+  npy_intp __pyx_r;
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":330
+ *         cdef inline npy_intp size(self) noexcept nogil:
+ *             """The total broadcasted size."""
+ *             return PyArray_MultiIter_SIZE(self)             # <<<<<<<<<<<<<<
+ * 
+ *         @property
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+  __pyx_r = PyArray_MultiIter_SIZE(__pyx_v_self);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":328
+ * 
+ *         @property
+ *         cdef inline npy_intp size(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The total broadcasted size."""
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+ */
+
+  /* function exit code */
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+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":333
+ * 
+ *         @property
+ *         cdef inline npy_intp index(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The current (1-d) index into the broadcasted result."""
+ *             return PyArray_MultiIter_INDEX(self)
+ */
+
+static CYTHON_INLINE npy_intp __pyx_f_5numpy_9broadcast_5index_index(PyArrayMultiIterObject *__pyx_v_self) {
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":335
+ *         cdef inline npy_intp index(self) noexcept nogil:
+ *             """The current (1-d) index into the broadcasted result."""
+ *             return PyArray_MultiIter_INDEX(self)             # <<<<<<<<<<<<<<
+ * 
+ *         @property
+ */
+  __pyx_r = PyArray_MultiIter_INDEX(__pyx_v_self);
+  goto __pyx_L0;
+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":333
+ * 
+ *         @property
+ *         cdef inline npy_intp index(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The current (1-d) index into the broadcasted result."""
+ *             return PyArray_MultiIter_INDEX(self)
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+
+  /* function exit code */
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+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":338
+ * 
+ *         @property
+ *         cdef inline int nd(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The number of dimensions in the broadcasted result."""
+ *             return PyArray_MultiIter_NDIM(self)
+ */
+
+static CYTHON_INLINE int __pyx_f_5numpy_9broadcast_2nd_nd(PyArrayMultiIterObject *__pyx_v_self) {
+  int __pyx_r;
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":340
+ *         cdef inline int nd(self) noexcept nogil:
+ *             """The number of dimensions in the broadcasted result."""
+ *             return PyArray_MultiIter_NDIM(self)             # <<<<<<<<<<<<<<
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+
+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":338
+ * 
+ *         @property
+ *         cdef inline int nd(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The number of dimensions in the broadcasted result."""
+ *             return PyArray_MultiIter_NDIM(self)
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+
+  /* function exit code */
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+  return __pyx_r;
+}
+
+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":343
+ * 
+ *         @property
+ *         cdef inline npy_intp* dimensions(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """The shape of the broadcasted result."""
+ *             return PyArray_MultiIter_DIMS(self)
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+static CYTHON_INLINE npy_intp *__pyx_f_5numpy_9broadcast_10dimensions_dimensions(PyArrayMultiIterObject *__pyx_v_self) {
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":345
+ *         cdef inline npy_intp* dimensions(self) noexcept nogil:
+ *             """The shape of the broadcasted result."""
+ *             return PyArray_MultiIter_DIMS(self)             # <<<<<<<<<<<<<<
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+  goto __pyx_L0;
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":343
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+ *         @property
+ *         cdef inline npy_intp* dimensions(self) noexcept nogil:             # <<<<<<<<<<<<<<
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+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":348
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":348
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+ *         @property
+ *         cdef inline PyObject* base(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """Returns a borrowed reference to the object owning the data/memory.
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+static CYTHON_INLINE PyObject *__pyx_f_5numpy_7ndarray_4base_base(PyArrayObject *__pyx_v_self) {
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":369
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+ *             return PyArray_BASE(self)             # <<<<<<<<<<<<<<
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+ *         @property
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":366
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+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":372
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+ *             """Returns an owned reference to the dtype of the array.
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+static CYTHON_INLINE PyArray_Descr *__pyx_f_5numpy_7ndarray_5descr_descr(PyArrayObject *__pyx_v_self) {
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":372
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+ *         cdef inline int ndim(self) noexcept nogil:             # <<<<<<<<<<<<<<
+ *             """Returns the number of dimensions in the array.
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+ */
+
+static CYTHON_INLINE int __pyx_f_5numpy_7ndarray_4ndim_ndim(PyArrayObject *__pyx_v_self) {
+  int __pyx_r;
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":381
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":378
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+  /* function exit code */
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+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":384
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":389
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":384
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+ *         @property
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+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":392
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+ *             """Returns a pointer to the strides of the array.
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+static CYTHON_INLINE npy_intp *__pyx_f_5numpy_7ndarray_7strides_strides(PyArrayObject *__pyx_v_self) {
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":396
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+  /* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":392
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+}
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+/* "../../../.local/lib/python3.10/site-packages/numpy/__init__.cython-30.pxd":399
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+} /* anonymous namespace */
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+#define __Pyx_PyMODINIT_FUNC extern "C" void
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+  #endif
+}
+/* #### Code section: cleanup_globals ### */
+/* #### Code section: cleanup_module ### */
+/* #### Code section: main_method ### */
+/* #### Code section: utility_code_pragmas ### */
+#ifdef _MSC_VER
+#pragma warning( push )
+/* Warning 4127: conditional expression is constant
+ * Cython uses constant conditional expressions to allow in inline functions to be optimized at
+ * compile-time, so this warning is not useful
+ */
+#pragma warning( disable : 4127 )
+#endif
+
+
+
+/* #### Code section: utility_code_def ### */
+
+/* --- Runtime support code --- */
+/* Refnanny */
+#if CYTHON_REFNANNY
+static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
+    PyObject *m = NULL, *p = NULL;
+    void *r = NULL;
+    m = PyImport_ImportModule(modname);
+    if (!m) goto end;
+    p = PyObject_GetAttrString(m, "RefNannyAPI");
+    if (!p) goto end;
+    r = PyLong_AsVoidPtr(p);
+end:
+    Py_XDECREF(p);
+    Py_XDECREF(m);
+    return (__Pyx_RefNannyAPIStruct *)r;
+}
+#endif
+
+/* PyErrExceptionMatches */
+#if CYTHON_FAST_THREAD_STATE
+static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
+    Py_ssize_t i, n;
+    n = PyTuple_GET_SIZE(tuple);
+#if PY_MAJOR_VERSION >= 3
+    for (i=0; i<n; i++) {
+        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
+    }
+#endif
+    for (i=0; i<n; i++) {
+        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
+    }
+    return 0;
+}
+static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
+    int result;
+    PyObject *exc_type;
+#if PY_VERSION_HEX >= 0x030C00A6
+    PyObject *current_exception = tstate->current_exception;
+    if (unlikely(!current_exception)) return 0;
+    exc_type = (PyObject*) Py_TYPE(current_exception);
+    if (exc_type == err) return 1;
+#else
+    exc_type = tstate->curexc_type;
+    if (exc_type == err) return 1;
+    if (unlikely(!exc_type)) return 0;
+#endif
+    #if CYTHON_AVOID_BORROWED_REFS
+    Py_INCREF(exc_type);
+    #endif
+    if (unlikely(PyTuple_Check(err))) {
+        result = __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
+    } else {
+        result = __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
+    }
+    #if CYTHON_AVOID_BORROWED_REFS
+    Py_DECREF(exc_type);
+    #endif
+    return result;
+}
+#endif
+
+/* PyErrFetchRestore */
+#if CYTHON_FAST_THREAD_STATE
+static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
+#if PY_VERSION_HEX >= 0x030C00A6
+    PyObject *tmp_value;
+    assert(type == NULL || (value != NULL && type == (PyObject*) Py_TYPE(value)));
+    if (value) {
+        #if CYTHON_COMPILING_IN_CPYTHON
+        if (unlikely(((PyBaseExceptionObject*) value)->traceback != tb))
+        #endif
+            PyException_SetTraceback(value, tb);
+    }
+    tmp_value = tstate->current_exception;
+    tstate->current_exception = value;
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(type);
+    Py_XDECREF(tb);
+#else
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    tmp_type = tstate->curexc_type;
+    tmp_value = tstate->curexc_value;
+    tmp_tb = tstate->curexc_traceback;
+    tstate->curexc_type = type;
+    tstate->curexc_value = value;
+    tstate->curexc_traceback = tb;
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+#endif
+}
+static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
+#if PY_VERSION_HEX >= 0x030C00A6
+    PyObject* exc_value;
+    exc_value = tstate->current_exception;
+    tstate->current_exception = 0;
+    *value = exc_value;
+    *type = NULL;
+    *tb = NULL;
+    if (exc_value) {
+        *type = (PyObject*) Py_TYPE(exc_value);
+        Py_INCREF(*type);
+        #if CYTHON_COMPILING_IN_CPYTHON
+        *tb = ((PyBaseExceptionObject*) exc_value)->traceback;
+        Py_XINCREF(*tb);
+        #else
+        *tb = PyException_GetTraceback(exc_value);
+        #endif
+    }
+#else
+    *type = tstate->curexc_type;
+    *value = tstate->curexc_value;
+    *tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+#endif
+}
+#endif
+
+/* PyObjectGetAttrStr */
+#if CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
+    PyTypeObject* tp = Py_TYPE(obj);
+    if (likely(tp->tp_getattro))
+        return tp->tp_getattro(obj, attr_name);
+#if PY_MAJOR_VERSION < 3
+    if (likely(tp->tp_getattr))
+        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
+#endif
+    return PyObject_GetAttr(obj, attr_name);
+}
+#endif
+
+/* PyObjectGetAttrStrNoError */
+#if __PYX_LIMITED_VERSION_HEX < 0x030d00A1
+static void __Pyx_PyObject_GetAttrStr_ClearAttributeError(void) {
+    __Pyx_PyThreadState_declare
+    __Pyx_PyThreadState_assign
+    if (likely(__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError)))
+        __Pyx_PyErr_Clear();
+}
+#endif
+static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name) {
+    PyObject *result;
+#if __PYX_LIMITED_VERSION_HEX >= 0x030d00A1
+    (void) PyObject_GetOptionalAttr(obj, attr_name, &result);
+    return result;
+#else
+#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_TYPE_SLOTS && PY_VERSION_HEX >= 0x030700B1
+    PyTypeObject* tp = Py_TYPE(obj);
+    if (likely(tp->tp_getattro == PyObject_GenericGetAttr)) {
+        return _PyObject_GenericGetAttrWithDict(obj, attr_name, NULL, 1);
+    }
+#endif
+    result = __Pyx_PyObject_GetAttrStr(obj, attr_name);
+    if (unlikely(!result)) {
+        __Pyx_PyObject_GetAttrStr_ClearAttributeError();
+    }
+    return result;
+#endif
+}
+
+/* GetBuiltinName */
+static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
+    PyObject* result = __Pyx_PyObject_GetAttrStrNoError(__pyx_b, name);
+    if (unlikely(!result) && !PyErr_Occurred()) {
+        PyErr_Format(PyExc_NameError,
+#if PY_MAJOR_VERSION >= 3
+            "name '%U' is not defined", name);
+#else
+            "name '%.200s' is not defined", PyString_AS_STRING(name));
+#endif
+    }
+    return result;
+}
+
+/* GetTopmostException */
+#if CYTHON_USE_EXC_INFO_STACK && CYTHON_FAST_THREAD_STATE
+static _PyErr_StackItem *
+__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
+{
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    while ((exc_info->exc_value == NULL || exc_info->exc_value == Py_None) &&
+           exc_info->previous_item != NULL)
+    {
+        exc_info = exc_info->previous_item;
+    }
+    return exc_info;
+}
+#endif
+
+/* SaveResetException */
+#if CYTHON_FAST_THREAD_STATE
+static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
+  #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4
+    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
+    PyObject *exc_value = exc_info->exc_value;
+    if (exc_value == NULL || exc_value == Py_None) {
+        *value = NULL;
+        *type = NULL;
+        *tb = NULL;
+    } else {
+        *value = exc_value;
+        Py_INCREF(*value);
+        *type = (PyObject*) Py_TYPE(exc_value);
+        Py_INCREF(*type);
+        *tb = PyException_GetTraceback(exc_value);
+    }
+  #elif CYTHON_USE_EXC_INFO_STACK
+    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
+    *type = exc_info->exc_type;
+    *value = exc_info->exc_value;
+    *tb = exc_info->exc_traceback;
+    Py_XINCREF(*type);
+    Py_XINCREF(*value);
+    Py_XINCREF(*tb);
+  #else
+    *type = tstate->exc_type;
+    *value = tstate->exc_value;
+    *tb = tstate->exc_traceback;
+    Py_XINCREF(*type);
+    Py_XINCREF(*value);
+    Py_XINCREF(*tb);
+  #endif
+}
+static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
+  #if CYTHON_USE_EXC_INFO_STACK && PY_VERSION_HEX >= 0x030B00a4
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    PyObject *tmp_value = exc_info->exc_value;
+    exc_info->exc_value = value;
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(type);
+    Py_XDECREF(tb);
+  #else
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+    #if CYTHON_USE_EXC_INFO_STACK
+    _PyErr_StackItem *exc_info = tstate->exc_info;
+    tmp_type = exc_info->exc_type;
+    tmp_value = exc_info->exc_value;
+    tmp_tb = exc_info->exc_traceback;
+    exc_info->exc_type = type;
+    exc_info->exc_value = value;
+    exc_info->exc_traceback = tb;
+    #else
+    tmp_type = tstate->exc_type;
+    tmp_value = tstate->exc_value;
+    tmp_tb = tstate->exc_traceback;
+    tstate->exc_type = type;
+    tstate->exc_value = value;
+    tstate->exc_traceback = tb;
+    #endif
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+  #endif
+}
+#endif
+
+/* GetException */
+#if CYTHON_FAST_THREAD_STATE
+static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
+#else
+static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
+#endif
+{
+    PyObject *local_type = NULL, *local_value, *local_tb = NULL;
+#if CYTHON_FAST_THREAD_STATE
+    PyObject *tmp_type, *tmp_value, *tmp_tb;
+  #if PY_VERSION_HEX >= 0x030C00A6
+    local_value = tstate->current_exception;
+    tstate->current_exception = 0;
+    if (likely(local_value)) {
+        local_type = (PyObject*) Py_TYPE(local_value);
+        Py_INCREF(local_type);
+        local_tb = PyException_GetTraceback(local_value);
+    }
+  #else
+    local_type = tstate->curexc_type;
+    local_value = tstate->curexc_value;
+    local_tb = tstate->curexc_traceback;
+    tstate->curexc_type = 0;
+    tstate->curexc_value = 0;
+    tstate->curexc_traceback = 0;
+  #endif
+#else
+    PyErr_Fetch(&local_type, &local_value, &local_tb);
+#endif
+    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
+#if CYTHON_FAST_THREAD_STATE && PY_VERSION_HEX >= 0x030C00A6
+    if (unlikely(tstate->current_exception))
+#elif CYTHON_FAST_THREAD_STATE
+    if (unlikely(tstate->curexc_type))
+#else
+    if (unlikely(PyErr_Occurred()))
+#endif
+        goto bad;
+    #if PY_MAJOR_VERSION >= 3
+    if (local_tb) {
+        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
+            goto bad;
+    }
+    #endif
+    Py_XINCREF(local_tb);
+    Py_XINCREF(local_type);
+    Py_XINCREF(local_value);
+    *type = local_type;
+    *value = local_value;
+    *tb = local_tb;
+#if CYTHON_FAST_THREAD_STATE
+    #if CYTHON_USE_EXC_INFO_STACK
+    {
+        _PyErr_StackItem *exc_info = tstate->exc_info;
+      #if PY_VERSION_HEX >= 0x030B00a4
+        tmp_value = exc_info->exc_value;
+        exc_info->exc_value = local_value;
+        tmp_type = NULL;
+        tmp_tb = NULL;
+        Py_XDECREF(local_type);
+        Py_XDECREF(local_tb);
+      #else
+        tmp_type = exc_info->exc_type;
+        tmp_value = exc_info->exc_value;
+        tmp_tb = exc_info->exc_traceback;
+        exc_info->exc_type = local_type;
+        exc_info->exc_value = local_value;
+        exc_info->exc_traceback = local_tb;
+      #endif
+    }
+    #else
+    tmp_type = tstate->exc_type;
+    tmp_value = tstate->exc_value;
+    tmp_tb = tstate->exc_traceback;
+    tstate->exc_type = local_type;
+    tstate->exc_value = local_value;
+    tstate->exc_traceback = local_tb;
+    #endif
+    Py_XDECREF(tmp_type);
+    Py_XDECREF(tmp_value);
+    Py_XDECREF(tmp_tb);
+#else
+    PyErr_SetExcInfo(local_type, local_value, local_tb);
+#endif
+    return 0;
+bad:
+    *type = 0;
+    *value = 0;
+    *tb = 0;
+    Py_XDECREF(local_type);
+    Py_XDECREF(local_value);
+    Py_XDECREF(local_tb);
+    return -1;
+}
+
+/* PyObjectCall */
+#if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
+    PyObject *result;
+    ternaryfunc call = Py_TYPE(func)->tp_call;
+    if (unlikely(!call))
+        return PyObject_Call(func, arg, kw);
+    #if PY_MAJOR_VERSION < 3
+    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
+        return NULL;
+    #else
+    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object")))
+        return NULL;
+    #endif
+    result = (*call)(func, arg, kw);
+    Py_LeaveRecursiveCall();
+    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
+        PyErr_SetString(
+            PyExc_SystemError,
+            "NULL result without error in PyObject_Call");
+    }
+    return result;
+}
+#endif
+
+/* RaiseException */
+#if PY_MAJOR_VERSION < 3
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
+    __Pyx_PyThreadState_declare
+    CYTHON_UNUSED_VAR(cause);
+    Py_XINCREF(type);
+    if (!value || value == Py_None)
+        value = NULL;
+    else
+        Py_INCREF(value);
+    if (!tb || tb == Py_None)
+        tb = NULL;
+    else {
+        Py_INCREF(tb);
+        if (!PyTraceBack_Check(tb)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: arg 3 must be a traceback or None");
+            goto raise_error;
+        }
+    }
+    if (PyType_Check(type)) {
+#if CYTHON_COMPILING_IN_PYPY
+        if (!value) {
+            Py_INCREF(Py_None);
+            value = Py_None;
+        }
+#endif
+        PyErr_NormalizeException(&type, &value, &tb);
+    } else {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto raise_error;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(type);
+        Py_INCREF(type);
+        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
+            PyErr_SetString(PyExc_TypeError,
+                "raise: exception class must be a subclass of BaseException");
+            goto raise_error;
+        }
+    }
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrRestore(type, value, tb);
+    return;
+raise_error:
+    Py_XDECREF(value);
+    Py_XDECREF(type);
+    Py_XDECREF(tb);
+    return;
+}
+#else
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
+    PyObject* owned_instance = NULL;
+    if (tb == Py_None) {
+        tb = 0;
+    } else if (tb && !PyTraceBack_Check(tb)) {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: arg 3 must be a traceback or None");
+        goto bad;
+    }
+    if (value == Py_None)
+        value = 0;
+    if (PyExceptionInstance_Check(type)) {
+        if (value) {
+            PyErr_SetString(PyExc_TypeError,
+                "instance exception may not have a separate value");
+            goto bad;
+        }
+        value = type;
+        type = (PyObject*) Py_TYPE(value);
+    } else if (PyExceptionClass_Check(type)) {
+        PyObject *instance_class = NULL;
+        if (value && PyExceptionInstance_Check(value)) {
+            instance_class = (PyObject*) Py_TYPE(value);
+            if (instance_class != type) {
+                int is_subclass = PyObject_IsSubclass(instance_class, type);
+                if (!is_subclass) {
+                    instance_class = NULL;
+                } else if (unlikely(is_subclass == -1)) {
+                    goto bad;
+                } else {
+                    type = instance_class;
+                }
+            }
+        }
+        if (!instance_class) {
+            PyObject *args;
+            if (!value)
+                args = PyTuple_New(0);
+            else if (PyTuple_Check(value)) {
+                Py_INCREF(value);
+                args = value;
+            } else
+                args = PyTuple_Pack(1, value);
+            if (!args)
+                goto bad;
+            owned_instance = PyObject_Call(type, args, NULL);
+            Py_DECREF(args);
+            if (!owned_instance)
+                goto bad;
+            value = owned_instance;
+            if (!PyExceptionInstance_Check(value)) {
+                PyErr_Format(PyExc_TypeError,
+                             "calling %R should have returned an instance of "
+                             "BaseException, not %R",
+                             type, Py_TYPE(value));
+                goto bad;
+            }
+        }
+    } else {
+        PyErr_SetString(PyExc_TypeError,
+            "raise: exception class must be a subclass of BaseException");
+        goto bad;
+    }
+    if (cause) {
+        PyObject *fixed_cause;
+        if (cause == Py_None) {
+            fixed_cause = NULL;
+        } else if (PyExceptionClass_Check(cause)) {
+            fixed_cause = PyObject_CallObject(cause, NULL);
+            if (fixed_cause == NULL)
+                goto bad;
+        } else if (PyExceptionInstance_Check(cause)) {
+            fixed_cause = cause;
+            Py_INCREF(fixed_cause);
+        } else {
+            PyErr_SetString(PyExc_TypeError,
+                            "exception causes must derive from "
+                            "BaseException");
+            goto bad;
+        }
+        PyException_SetCause(value, fixed_cause);
+    }
+    PyErr_SetObject(type, value);
+    if (tb) {
+      #if PY_VERSION_HEX >= 0x030C00A6
+        PyException_SetTraceback(value, tb);
+      #elif CYTHON_FAST_THREAD_STATE
+        PyThreadState *tstate = __Pyx_PyThreadState_Current;
+        PyObject* tmp_tb = tstate->curexc_traceback;
+        if (tb != tmp_tb) {
+            Py_INCREF(tb);
+            tstate->curexc_traceback = tb;
+            Py_XDECREF(tmp_tb);
+        }
+#else
+        PyObject *tmp_type, *tmp_value, *tmp_tb;
+        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
+        Py_INCREF(tb);
+        PyErr_Restore(tmp_type, tmp_value, tb);
+        Py_XDECREF(tmp_tb);
+#endif
+    }
+bad:
+    Py_XDECREF(owned_instance);
+    return;
+}
+#endif
+
+/* IsLittleEndian */
+static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
+{
+  union {
+    uint32_t u32;
+    uint8_t u8[4];
+  } S;
+  S.u32 = 0x01020304;
+  return S.u8[0] == 4;
+}
+
+/* BufferFormatCheck */
+static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
+                              __Pyx_BufFmt_StackElem* stack,
+                              __Pyx_TypeInfo* type) {
+  stack[0].field = &ctx->root;
+  stack[0].parent_offset = 0;
+  ctx->root.type = type;
+  ctx->root.name = "buffer dtype";
+  ctx->root.offset = 0;
+  ctx->head = stack;
+  ctx->head->field = &ctx->root;
+  ctx->fmt_offset = 0;
+  ctx->head->parent_offset = 0;
+  ctx->new_packmode = '@';
+  ctx->enc_packmode = '@';
+  ctx->new_count = 1;
+  ctx->enc_count = 0;
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  ctx->is_valid_array = 0;
+  ctx->struct_alignment = 0;
+  while (type->typegroup == 'S') {
+    ++ctx->head;
+    ctx->head->field = type->fields;
+    ctx->head->parent_offset = 0;
+    type = type->fields->type;
+  }
+}
+static int __Pyx_BufFmt_ParseNumber(const char** ts) {
+    int count;
+    const char* t = *ts;
+    if (*t < '0' || *t > '9') {
+      return -1;
+    } else {
+        count = *t++ - '0';
+        while (*t >= '0' && *t <= '9') {
+            count *= 10;
+            count += *t++ - '0';
+        }
+    }
+    *ts = t;
+    return count;
+}
+static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
+    int number = __Pyx_BufFmt_ParseNumber(ts);
+    if (number == -1)
+        PyErr_Format(PyExc_ValueError,\
+                     "Does not understand character buffer dtype format string ('%c')", **ts);
+    return number;
+}
+static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
+  PyErr_Format(PyExc_ValueError,
+               "Unexpected format string character: '%c'", ch);
+}
+static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
+  switch (ch) {
+    case '?': return "'bool'";
+    case 'c': return "'char'";
+    case 'b': return "'signed char'";
+    case 'B': return "'unsigned char'";
+    case 'h': return "'short'";
+    case 'H': return "'unsigned short'";
+    case 'i': return "'int'";
+    case 'I': return "'unsigned int'";
+    case 'l': return "'long'";
+    case 'L': return "'unsigned long'";
+    case 'q': return "'long long'";
+    case 'Q': return "'unsigned long long'";
+    case 'f': return (is_complex ? "'complex float'" : "'float'");
+    case 'd': return (is_complex ? "'complex double'" : "'double'");
+    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
+    case 'T': return "a struct";
+    case 'O': return "Python object";
+    case 'P': return "a pointer";
+    case 's': case 'p': return "a string";
+    case 0: return "end";
+    default: return "unparsable format string";
+  }
+}
+static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return 2;
+    case 'i': case 'I': case 'l': case 'L': return 4;
+    case 'q': case 'Q': return 8;
+    case 'f': return (is_complex ? 8 : 4);
+    case 'd': return (is_complex ? 16 : 8);
+    case 'g': {
+      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
+      return 0;
+    }
+    case 'O': case 'P': return sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(short);
+    case 'i': case 'I': return sizeof(int);
+    case 'l': case 'L': return sizeof(long);
+    #ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
+    #endif
+    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
+    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
+    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
+    case 'O': case 'P': return sizeof(void*);
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+typedef struct { char c; short x; } __Pyx_st_short;
+typedef struct { char c; int x; } __Pyx_st_int;
+typedef struct { char c; long x; } __Pyx_st_long;
+typedef struct { char c; float x; } __Pyx_st_float;
+typedef struct { char c; double x; } __Pyx_st_double;
+typedef struct { char c; long double x; } __Pyx_st_longdouble;
+typedef struct { char c; void *x; } __Pyx_st_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, int is_complex) {
+  CYTHON_UNUSED_VAR(is_complex);
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+/* These are for computing the padding at the end of the struct to align
+   on the first member of the struct. This will probably the same as above,
+   but we don't have any guarantees.
+ */
+typedef struct { short x; char c; } __Pyx_pad_short;
+typedef struct { int x; char c; } __Pyx_pad_int;
+typedef struct { long x; char c; } __Pyx_pad_long;
+typedef struct { float x; char c; } __Pyx_pad_float;
+typedef struct { double x; char c; } __Pyx_pad_double;
+typedef struct { long double x; char c; } __Pyx_pad_longdouble;
+typedef struct { void *x; char c; } __Pyx_pad_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
+#endif
+static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, int is_complex) {
+  CYTHON_UNUSED_VAR(is_complex);
+  switch (ch) {
+    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
+    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
+    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
+    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
+#endif
+    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
+    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
+    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
+    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
+    default:
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+}
+static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
+  switch (ch) {
+    case 'c':
+        return 'H';
+    case 'b': case 'h': case 'i':
+    case 'l': case 'q': case 's': case 'p':
+        return 'I';
+    case '?': case 'B': case 'H': case 'I': case 'L': case 'Q':
+        return 'U';
+    case 'f': case 'd': case 'g':
+        return (is_complex ? 'C' : 'R');
+    case 'O':
+        return 'O';
+    case 'P':
+        return 'P';
+    default: {
+      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+      return 0;
+    }
+  }
+}
+static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
+  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
+    const char* expected;
+    const char* quote;
+    if (ctx->head == NULL) {
+      expected = "end";
+      quote = "";
+    } else {
+      expected = ctx->head->field->type->name;
+      quote = "'";
+    }
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected %s%s%s but got %s",
+                 quote, expected, quote,
+                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
+  } else {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_StructField* parent = (ctx->head - 1)->field;
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
+                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
+                 parent->type->name, field->name);
+  }
+}
+static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
+  char group;
+  size_t size, offset, arraysize = 1;
+  if (ctx->enc_type == 0) return 0;
+  if (ctx->head->field->type->arraysize[0]) {
+    int i, ndim = 0;
+    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
+        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
+        ndim = 1;
+        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
+            PyErr_Format(PyExc_ValueError,
+                         "Expected a dimension of size %zu, got %zu",
+                         ctx->head->field->type->arraysize[0], ctx->enc_count);
+            return -1;
+        }
+    }
+    if (!ctx->is_valid_array) {
+      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
+                   ctx->head->field->type->ndim, ndim);
+      return -1;
+    }
+    for (i = 0; i < ctx->head->field->type->ndim; i++) {
+      arraysize *= ctx->head->field->type->arraysize[i];
+    }
+    ctx->is_valid_array = 0;
+    ctx->enc_count = 1;
+  }
+  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
+  do {
+    __Pyx_StructField* field = ctx->head->field;
+    __Pyx_TypeInfo* type = field->type;
+    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
+      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
+    } else {
+      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
+    }
+    if (ctx->enc_packmode == '@') {
+      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
+      size_t align_mod_offset;
+      if (align_at == 0) return -1;
+      align_mod_offset = ctx->fmt_offset % align_at;
+      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
+      if (ctx->struct_alignment == 0)
+          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
+                                                                 ctx->is_complex);
+    }
+    if (type->size != size || type->typegroup != group) {
+      if (type->typegroup == 'C' && type->fields != NULL) {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        ++ctx->head;
+        ctx->head->field = type->fields;
+        ctx->head->parent_offset = parent_offset;
+        continue;
+      }
+      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
+      } else {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+      }
+    }
+    offset = ctx->head->parent_offset + field->offset;
+    if (ctx->fmt_offset != offset) {
+      PyErr_Format(PyExc_ValueError,
+                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
+                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
+      return -1;
+    }
+    ctx->fmt_offset += size;
+    if (arraysize)
+      ctx->fmt_offset += (arraysize - 1) * size;
+    --ctx->enc_count;
+    while (1) {
+      if (field == &ctx->root) {
+        ctx->head = NULL;
+        if (ctx->enc_count != 0) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return -1;
+        }
+        break;
+      }
+      ctx->head->field = ++field;
+      if (field->type == NULL) {
+        --ctx->head;
+        field = ctx->head->field;
+        continue;
+      } else if (field->type->typegroup == 'S') {
+        size_t parent_offset = ctx->head->parent_offset + field->offset;
+        if (field->type->fields->type == NULL) continue;
+        field = field->type->fields;
+        ++ctx->head;
+        ctx->head->field = field;
+        ctx->head->parent_offset = parent_offset;
+        break;
+      } else {
+        break;
+      }
+    }
+  } while (ctx->enc_count);
+  ctx->enc_type = 0;
+  ctx->is_complex = 0;
+  return 0;
+}
+static int
+__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
+{
+    const char *ts = *tsp;
+    int i = 0, number, ndim;
+    ++ts;
+    if (ctx->new_count != 1) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Cannot handle repeated arrays in format string");
+        return -1;
+    }
+    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return -1;
+    ndim = ctx->head->field->type->ndim;
+    while (*ts && *ts != ')') {
+        switch (*ts) {
+            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
+            default:  break;
+        }
+        number = __Pyx_BufFmt_ExpectNumber(&ts);
+        if (number == -1) return -1;
+        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i]) {
+            PyErr_Format(PyExc_ValueError,
+                        "Expected a dimension of size %zu, got %d",
+                        ctx->head->field->type->arraysize[i], number);
+            return -1;
+        }
+        if (*ts != ',' && *ts != ')') {
+            PyErr_Format(PyExc_ValueError,
+                                "Expected a comma in format string, got '%c'", *ts);
+            return -1;
+        }
+        if (*ts == ',') ts++;
+        i++;
+    }
+    if (i != ndim) {
+        PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
+                            ctx->head->field->type->ndim, i);
+        return -1;
+    }
+    if (!*ts) {
+        PyErr_SetString(PyExc_ValueError,
+                        "Unexpected end of format string, expected ')'");
+        return -1;
+    }
+    ctx->is_valid_array = 1;
+    ctx->new_count = 1;
+    *tsp = ++ts;
+    return 0;
+}
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
+  int got_Z = 0;
+  while (1) {
+    switch(*ts) {
+      case 0:
+        if (ctx->enc_type != 0 && ctx->head == NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        if (ctx->head != NULL) {
+          __Pyx_BufFmt_RaiseExpected(ctx);
+          return NULL;
+        }
+        return ts;
+      case ' ':
+      case '\r':
+      case '\n':
+        ++ts;
+        break;
+      case '<':
+        if (!__Pyx_Is_Little_Endian()) {
+          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '>':
+      case '!':
+        if (__Pyx_Is_Little_Endian()) {
+          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
+          return NULL;
+        }
+        ctx->new_packmode = '=';
+        ++ts;
+        break;
+      case '=':
+      case '@':
+      case '^':
+        ctx->new_packmode = *ts++;
+        break;
+      case 'T':
+        {
+          const char* ts_after_sub;
+          size_t i, struct_count = ctx->new_count;
+          size_t struct_alignment = ctx->struct_alignment;
+          ctx->new_count = 1;
+          ++ts;
+          if (*ts != '{') {
+            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
+            return NULL;
+          }
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          ctx->enc_count = 0;
+          ctx->struct_alignment = 0;
+          ++ts;
+          ts_after_sub = ts;
+          for (i = 0; i != struct_count; ++i) {
+            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
+            if (!ts_after_sub) return NULL;
+          }
+          ts = ts_after_sub;
+          if (struct_alignment) ctx->struct_alignment = struct_alignment;
+        }
+        break;
+      case '}':
+        {
+          size_t alignment = ctx->struct_alignment;
+          ++ts;
+          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+          ctx->enc_type = 0;
+          if (alignment && ctx->fmt_offset % alignment) {
+            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
+          }
+        }
+        return ts;
+      case 'x':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->fmt_offset += ctx->new_count;
+        ctx->new_count = 1;
+        ctx->enc_count = 0;
+        ctx->enc_type = 0;
+        ctx->enc_packmode = ctx->new_packmode;
+        ++ts;
+        break;
+      case 'Z':
+        got_Z = 1;
+        ++ts;
+        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
+          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
+          return NULL;
+        }
+        CYTHON_FALLTHROUGH;
+      case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
+      case 'l': case 'L': case 'q': case 'Q':
+      case 'f': case 'd': case 'g':
+      case 'O': case 'p':
+        if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) &&
+            (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) {
+          ctx->enc_count += ctx->new_count;
+          ctx->new_count = 1;
+          got_Z = 0;
+          ++ts;
+          break;
+        }
+        CYTHON_FALLTHROUGH;
+      case 's':
+        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+        ctx->enc_count = ctx->new_count;
+        ctx->enc_packmode = ctx->new_packmode;
+        ctx->enc_type = *ts;
+        ctx->is_complex = got_Z;
+        ++ts;
+        ctx->new_count = 1;
+        got_Z = 0;
+        break;
+      case ':':
+        ++ts;
+        while(*ts != ':') ++ts;
+        ++ts;
+        break;
+      case '(':
+        if (__pyx_buffmt_parse_array(ctx, &ts) < 0) return NULL;
+        break;
+      default:
+        {
+          int number = __Pyx_BufFmt_ExpectNumber(&ts);
+          if (number == -1) return NULL;
+          ctx->new_count = (size_t)number;
+        }
+    }
+  }
+}
+
+/* BufferGetAndValidate */
+  static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
+  if (unlikely(info->buf == NULL)) return;
+  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
+  __Pyx_ReleaseBuffer(info);
+}
+static void __Pyx_ZeroBuffer(Py_buffer* buf) {
+  buf->buf = NULL;
+  buf->obj = NULL;
+  buf->strides = __Pyx_zeros;
+  buf->shape = __Pyx_zeros;
+  buf->suboffsets = __Pyx_minusones;
+}
+static int __Pyx__GetBufferAndValidate(
+        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
+        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
+{
+  buf->buf = NULL;
+  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
+    __Pyx_ZeroBuffer(buf);
+    return -1;
+  }
+  if (unlikely(buf->ndim != nd)) {
+    PyErr_Format(PyExc_ValueError,
+                 "Buffer has wrong number of dimensions (expected %d, got %d)",
+                 nd, buf->ndim);
+    goto fail;
+  }
+  if (!cast) {
+    __Pyx_BufFmt_Context ctx;
+    __Pyx_BufFmt_Init(&ctx, stack, dtype);
+    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
+  }
+  if (unlikely((size_t)buf->itemsize != dtype->size)) {
+    PyErr_Format(PyExc_ValueError,
+      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
+      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
+      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
+    goto fail;
+  }
+  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
+  return 0;
+fail:;
+  __Pyx_SafeReleaseBuffer(buf);
+  return -1;
+}
+
+/* BufferIndexError */
+  static void __Pyx_RaiseBufferIndexError(int axis) {
+  PyErr_Format(PyExc_IndexError,
+     "Out of bounds on buffer access (axis %d)", axis);
+}
+
+/* TupleAndListFromArray */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static CYTHON_INLINE void __Pyx_copy_object_array(PyObject *const *CYTHON_RESTRICT src, PyObject** CYTHON_RESTRICT dest, Py_ssize_t length) {
+    PyObject *v;
+    Py_ssize_t i;
+    for (i = 0; i < length; i++) {
+        v = dest[i] = src[i];
+        Py_INCREF(v);
+    }
+}
+static CYTHON_INLINE PyObject *
+__Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n)
+{
+    PyObject *res;
+    if (n <= 0) {
+        Py_INCREF(__pyx_empty_tuple);
+        return __pyx_empty_tuple;
+    }
+    res = PyTuple_New(n);
+    if (unlikely(res == NULL)) return NULL;
+    __Pyx_copy_object_array(src, ((PyTupleObject*)res)->ob_item, n);
+    return res;
+}
+static CYTHON_INLINE PyObject *
+__Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n)
+{
+    PyObject *res;
+    if (n <= 0) {
+        return PyList_New(0);
+    }
+    res = PyList_New(n);
+    if (unlikely(res == NULL)) return NULL;
+    __Pyx_copy_object_array(src, ((PyListObject*)res)->ob_item, n);
+    return res;
+}
+#endif
+
+/* BytesEquals */
+  static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
+#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API
+    return PyObject_RichCompareBool(s1, s2, equals);
+#else
+    if (s1 == s2) {
+        return (equals == Py_EQ);
+    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
+        const char *ps1, *ps2;
+        Py_ssize_t length = PyBytes_GET_SIZE(s1);
+        if (length != PyBytes_GET_SIZE(s2))
+            return (equals == Py_NE);
+        ps1 = PyBytes_AS_STRING(s1);
+        ps2 = PyBytes_AS_STRING(s2);
+        if (ps1[0] != ps2[0]) {
+            return (equals == Py_NE);
+        } else if (length == 1) {
+            return (equals == Py_EQ);
+        } else {
+            int result;
+#if CYTHON_USE_UNICODE_INTERNALS && (PY_VERSION_HEX < 0x030B0000)
+            Py_hash_t hash1, hash2;
+            hash1 = ((PyBytesObject*)s1)->ob_shash;
+            hash2 = ((PyBytesObject*)s2)->ob_shash;
+            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
+                return (equals == Py_NE);
+            }
+#endif
+            result = memcmp(ps1, ps2, (size_t)length);
+            return (equals == Py_EQ) ? (result == 0) : (result != 0);
+        }
+    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
+        return (equals == Py_NE);
+    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
+        return (equals == Py_NE);
+    } else {
+        int result;
+        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
+        if (!py_result)
+            return -1;
+        result = __Pyx_PyObject_IsTrue(py_result);
+        Py_DECREF(py_result);
+        return result;
+    }
+#endif
+}
+
+/* UnicodeEquals */
+  static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
+#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API
+    return PyObject_RichCompareBool(s1, s2, equals);
+#else
+#if PY_MAJOR_VERSION < 3
+    PyObject* owned_ref = NULL;
+#endif
+    int s1_is_unicode, s2_is_unicode;
+    if (s1 == s2) {
+        goto return_eq;
+    }
+    s1_is_unicode = PyUnicode_CheckExact(s1);
+    s2_is_unicode = PyUnicode_CheckExact(s2);
+#if PY_MAJOR_VERSION < 3
+    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
+        owned_ref = PyUnicode_FromObject(s2);
+        if (unlikely(!owned_ref))
+            return -1;
+        s2 = owned_ref;
+        s2_is_unicode = 1;
+    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
+        owned_ref = PyUnicode_FromObject(s1);
+        if (unlikely(!owned_ref))
+            return -1;
+        s1 = owned_ref;
+        s1_is_unicode = 1;
+    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
+        return __Pyx_PyBytes_Equals(s1, s2, equals);
+    }
+#endif
+    if (s1_is_unicode & s2_is_unicode) {
+        Py_ssize_t length;
+        int kind;
+        void *data1, *data2;
+        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
+            return -1;
+        length = __Pyx_PyUnicode_GET_LENGTH(s1);
+        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
+            goto return_ne;
+        }
+#if CYTHON_USE_UNICODE_INTERNALS
+        {
+            Py_hash_t hash1, hash2;
+        #if CYTHON_PEP393_ENABLED
+            hash1 = ((PyASCIIObject*)s1)->hash;
+            hash2 = ((PyASCIIObject*)s2)->hash;
+        #else
+            hash1 = ((PyUnicodeObject*)s1)->hash;
+            hash2 = ((PyUnicodeObject*)s2)->hash;
+        #endif
+            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
+                goto return_ne;
+            }
+        }
+#endif
+        kind = __Pyx_PyUnicode_KIND(s1);
+        if (kind != __Pyx_PyUnicode_KIND(s2)) {
+            goto return_ne;
+        }
+        data1 = __Pyx_PyUnicode_DATA(s1);
+        data2 = __Pyx_PyUnicode_DATA(s2);
+        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
+            goto return_ne;
+        } else if (length == 1) {
+            goto return_eq;
+        } else {
+            int result = memcmp(data1, data2, (size_t)(length * kind));
+            #if PY_MAJOR_VERSION < 3
+            Py_XDECREF(owned_ref);
+            #endif
+            return (equals == Py_EQ) ? (result == 0) : (result != 0);
+        }
+    } else if ((s1 == Py_None) & s2_is_unicode) {
+        goto return_ne;
+    } else if ((s2 == Py_None) & s1_is_unicode) {
+        goto return_ne;
+    } else {
+        int result;
+        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
+        #if PY_MAJOR_VERSION < 3
+        Py_XDECREF(owned_ref);
+        #endif
+        if (!py_result)
+            return -1;
+        result = __Pyx_PyObject_IsTrue(py_result);
+        Py_DECREF(py_result);
+        return result;
+    }
+return_eq:
+    #if PY_MAJOR_VERSION < 3
+    Py_XDECREF(owned_ref);
+    #endif
+    return (equals == Py_EQ);
+return_ne:
+    #if PY_MAJOR_VERSION < 3
+    Py_XDECREF(owned_ref);
+    #endif
+    return (equals == Py_NE);
+#endif
+}
+
+/* fastcall */
+  #if CYTHON_METH_FASTCALL
+static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s)
+{
+    Py_ssize_t i, n = PyTuple_GET_SIZE(kwnames);
+    for (i = 0; i < n; i++)
+    {
+        if (s == PyTuple_GET_ITEM(kwnames, i)) return kwvalues[i];
+    }
+    for (i = 0; i < n; i++)
+    {
+        int eq = __Pyx_PyUnicode_Equals(s, PyTuple_GET_ITEM(kwnames, i), Py_EQ);
+        if (unlikely(eq != 0)) {
+            if (unlikely(eq < 0)) return NULL;
+            return kwvalues[i];
+        }
+    }
+    return NULL;
+}
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000
+CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues) {
+    Py_ssize_t i, nkwargs = PyTuple_GET_SIZE(kwnames);
+    PyObject *dict;
+    dict = PyDict_New();
+    if (unlikely(!dict))
+        return NULL;
+    for (i=0; i<nkwargs; i++) {
+        PyObject *key = PyTuple_GET_ITEM(kwnames, i);
+        if (unlikely(PyDict_SetItem(dict, key, kwvalues[i]) < 0))
+            goto bad;
+    }
+    return dict;
+bad:
+    Py_DECREF(dict);
+    return NULL;
+}
+#endif
+#endif
+
+/* RaiseArgTupleInvalid */
+  static void __Pyx_RaiseArgtupleInvalid(
+    const char* func_name,
+    int exact,
+    Py_ssize_t num_min,
+    Py_ssize_t num_max,
+    Py_ssize_t num_found)
+{
+    Py_ssize_t num_expected;
+    const char *more_or_less;
+    if (num_found < num_min) {
+        num_expected = num_min;
+        more_or_less = "at least";
+    } else {
+        num_expected = num_max;
+        more_or_less = "at most";
+    }
+    if (exact) {
+        more_or_less = "exactly";
+    }
+    PyErr_Format(PyExc_TypeError,
+                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                 func_name, more_or_less, num_expected,
+                 (num_expected == 1) ? "" : "s", num_found);
+}
+
+/* RaiseDoubleKeywords */
+  static void __Pyx_RaiseDoubleKeywordsError(
+    const char* func_name,
+    PyObject* kw_name)
+{
+    PyErr_Format(PyExc_TypeError,
+        #if PY_MAJOR_VERSION >= 3
+        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
+        #else
+        "%s() got multiple values for keyword argument '%s'", func_name,
+        PyString_AsString(kw_name));
+        #endif
+}
+
+/* ParseKeywords */
+  static int __Pyx_ParseOptionalKeywords(
+    PyObject *kwds,
+    PyObject *const *kwvalues,
+    PyObject **argnames[],
+    PyObject *kwds2,
+    PyObject *values[],
+    Py_ssize_t num_pos_args,
+    const char* function_name)
+{
+    PyObject *key = 0, *value = 0;
+    Py_ssize_t pos = 0;
+    PyObject*** name;
+    PyObject*** first_kw_arg = argnames + num_pos_args;
+    int kwds_is_tuple = CYTHON_METH_FASTCALL && likely(PyTuple_Check(kwds));
+    while (1) {
+        Py_XDECREF(key); key = NULL;
+        Py_XDECREF(value); value = NULL;
+        if (kwds_is_tuple) {
+            Py_ssize_t size;
+#if CYTHON_ASSUME_SAFE_MACROS
+            size = PyTuple_GET_SIZE(kwds);
+#else
+            size = PyTuple_Size(kwds);
+            if (size < 0) goto bad;
+#endif
+            if (pos >= size) break;
+#if CYTHON_AVOID_BORROWED_REFS
+            key = __Pyx_PySequence_ITEM(kwds, pos);
+            if (!key) goto bad;
+#elif CYTHON_ASSUME_SAFE_MACROS
+            key = PyTuple_GET_ITEM(kwds, pos);
+#else
+            key = PyTuple_GetItem(kwds, pos);
+            if (!key) goto bad;
+#endif
+            value = kwvalues[pos];
+            pos++;
+        }
+        else
+        {
+            if (!PyDict_Next(kwds, &pos, &key, &value)) break;
+#if CYTHON_AVOID_BORROWED_REFS
+            Py_INCREF(key);
+#endif
+        }
+        name = first_kw_arg;
+        while (*name && (**name != key)) name++;
+        if (*name) {
+            values[name-argnames] = value;
+#if CYTHON_AVOID_BORROWED_REFS
+            Py_INCREF(value);
+            Py_DECREF(key);
+#endif
+            key = NULL;
+            value = NULL;
+            continue;
+        }
+#if !CYTHON_AVOID_BORROWED_REFS
+        Py_INCREF(key);
+#endif
+        Py_INCREF(value);
+        name = first_kw_arg;
+        #if PY_MAJOR_VERSION < 3
+        if (likely(PyString_Check(key))) {
+            while (*name) {
+                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
+                        && _PyString_Eq(**name, key)) {
+                    values[name-argnames] = value;
+#if CYTHON_AVOID_BORROWED_REFS
+                    value = NULL;
+#endif
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    if ((**argname == key) || (
+                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
+                             && _PyString_Eq(**argname, key))) {
+                        goto arg_passed_twice;
+                    }
+                    argname++;
+                }
+            }
+        } else
+        #endif
+        if (likely(PyUnicode_Check(key))) {
+            while (*name) {
+                int cmp = (
+                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                    (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
+                #endif
+                    PyUnicode_Compare(**name, key)
+                );
+                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                if (cmp == 0) {
+                    values[name-argnames] = value;
+#if CYTHON_AVOID_BORROWED_REFS
+                    value = NULL;
+#endif
+                    break;
+                }
+                name++;
+            }
+            if (*name) continue;
+            else {
+                PyObject*** argname = argnames;
+                while (argname != first_kw_arg) {
+                    int cmp = (**argname == key) ? 0 :
+                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
+                        (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
+                    #endif
+                        PyUnicode_Compare(**argname, key);
+                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
+                    if (cmp == 0) goto arg_passed_twice;
+                    argname++;
+                }
+            }
+        } else
+            goto invalid_keyword_type;
+        if (kwds2) {
+            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
+        } else {
+            goto invalid_keyword;
+        }
+    }
+    Py_XDECREF(key);
+    Py_XDECREF(value);
+    return 0;
+arg_passed_twice:
+    __Pyx_RaiseDoubleKeywordsError(function_name, key);
+    goto bad;
+invalid_keyword_type:
+    PyErr_Format(PyExc_TypeError,
+        "%.200s() keywords must be strings", function_name);
+    goto bad;
+invalid_keyword:
+    #if PY_MAJOR_VERSION < 3
+    PyErr_Format(PyExc_TypeError,
+        "%.200s() got an unexpected keyword argument '%.200s'",
+        function_name, PyString_AsString(key));
+    #else
+    PyErr_Format(PyExc_TypeError,
+        "%s() got an unexpected keyword argument '%U'",
+        function_name, key);
+    #endif
+bad:
+    Py_XDECREF(key);
+    Py_XDECREF(value);
+    return -1;
+}
+
+/* ArgTypeTest */
+  static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
+{
+    __Pyx_TypeName type_name;
+    __Pyx_TypeName obj_type_name;
+    if (unlikely(!type)) {
+        PyErr_SetString(PyExc_SystemError, "Missing type object");
+        return 0;
+    }
+    else if (exact) {
+        #if PY_MAJOR_VERSION == 2
+        if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
+        #endif
+    }
+    else {
+        if (likely(__Pyx_TypeCheck(obj, type))) return 1;
+    }
+    type_name = __Pyx_PyType_GetName(type);
+    obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj));
+    PyErr_Format(PyExc_TypeError,
+        "Argument '%.200s' has incorrect type (expected " __Pyx_FMT_TYPENAME
+        ", got " __Pyx_FMT_TYPENAME ")", name, type_name, obj_type_name);
+    __Pyx_DECREF_TypeName(type_name);
+    __Pyx_DECREF_TypeName(obj_type_name);
+    return 0;
+}
+
+/* TypeImport */
+  #ifndef __PYX_HAVE_RT_ImportType_3_0_11
+#define __PYX_HAVE_RT_ImportType_3_0_11
+static PyTypeObject *__Pyx_ImportType_3_0_11(PyObject *module, const char *module_name, const char *class_name,
+    size_t size, size_t alignment, enum __Pyx_ImportType_CheckSize_3_0_11 check_size)
+{
+    PyObject *result = 0;
+    char warning[200];
+    Py_ssize_t basicsize;
+    Py_ssize_t itemsize;
+#if CYTHON_COMPILING_IN_LIMITED_API
+    PyObject *py_basicsize;
+    PyObject *py_itemsize;
+#endif
+    result = PyObject_GetAttrString(module, class_name);
+    if (!result)
+        goto bad;
+    if (!PyType_Check(result)) {
+        PyErr_Format(PyExc_TypeError,
+            "%.200s.%.200s is not a type object",
+            module_name, class_name);
+        goto bad;
+    }
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    basicsize = ((PyTypeObject *)result)->tp_basicsize;
+    itemsize = ((PyTypeObject *)result)->tp_itemsize;
+#else
+    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
+    if (!py_basicsize)
+        goto bad;
+    basicsize = PyLong_AsSsize_t(py_basicsize);
+    Py_DECREF(py_basicsize);
+    py_basicsize = 0;
+    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
+        goto bad;
+    py_itemsize = PyObject_GetAttrString(result, "__itemsize__");
+    if (!py_itemsize)
+        goto bad;
+    itemsize = PyLong_AsSsize_t(py_itemsize);
+    Py_DECREF(py_itemsize);
+    py_itemsize = 0;
+    if (itemsize == (Py_ssize_t)-1 && PyErr_Occurred())
+        goto bad;
+#endif
+    if (itemsize) {
+        if (size % alignment) {
+            alignment = size % alignment;
+        }
+        if (itemsize < (Py_ssize_t)alignment)
+            itemsize = (Py_ssize_t)alignment;
+    }
+    if ((size_t)(basicsize + itemsize) < size) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize+itemsize);
+        goto bad;
+    }
+    if (check_size == __Pyx_ImportType_CheckSize_Error_3_0_11 &&
+            ((size_t)basicsize > size || (size_t)(basicsize + itemsize) < size)) {
+        PyErr_Format(PyExc_ValueError,
+            "%.200s.%.200s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd-%zd from PyObject",
+            module_name, class_name, size, basicsize, basicsize+itemsize);
+        goto bad;
+    }
+    else if (check_size == __Pyx_ImportType_CheckSize_Warn_3_0_11 && (size_t)basicsize > size) {
+        PyOS_snprintf(warning, sizeof(warning),
+            "%s.%s size changed, may indicate binary incompatibility. "
+            "Expected %zd from C header, got %zd from PyObject",
+            module_name, class_name, size, basicsize);
+        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
+    }
+    return (PyTypeObject *)result;
+bad:
+    Py_XDECREF(result);
+    return NULL;
+}
+#endif
+
+/* Import */
+  static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
+    PyObject *module = 0;
+    PyObject *empty_dict = 0;
+    PyObject *empty_list = 0;
+    #if PY_MAJOR_VERSION < 3
+    PyObject *py_import;
+    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
+    if (unlikely(!py_import))
+        goto bad;
+    if (!from_list) {
+        empty_list = PyList_New(0);
+        if (unlikely(!empty_list))
+            goto bad;
+        from_list = empty_list;
+    }
+    #endif
+    empty_dict = PyDict_New();
+    if (unlikely(!empty_dict))
+        goto bad;
+    {
+        #if PY_MAJOR_VERSION >= 3
+        if (level == -1) {
+            if (strchr(__Pyx_MODULE_NAME, '.') != NULL) {
+                module = PyImport_ImportModuleLevelObject(
+                    name, __pyx_d, empty_dict, from_list, 1);
+                if (unlikely(!module)) {
+                    if (unlikely(!PyErr_ExceptionMatches(PyExc_ImportError)))
+                        goto bad;
+                    PyErr_Clear();
+                }
+            }
+            level = 0;
+        }
+        #endif
+        if (!module) {
+            #if PY_MAJOR_VERSION < 3
+            PyObject *py_level = PyInt_FromLong(level);
+            if (unlikely(!py_level))
+                goto bad;
+            module = PyObject_CallFunctionObjArgs(py_import,
+                name, __pyx_d, empty_dict, from_list, py_level, (PyObject *)NULL);
+            Py_DECREF(py_level);
+            #else
+            module = PyImport_ImportModuleLevelObject(
+                name, __pyx_d, empty_dict, from_list, level);
+            #endif
+        }
+    }
+bad:
+    Py_XDECREF(empty_dict);
+    Py_XDECREF(empty_list);
+    #if PY_MAJOR_VERSION < 3
+    Py_XDECREF(py_import);
+    #endif
+    return module;
+}
+
+/* ImportDottedModule */
+  #if PY_MAJOR_VERSION >= 3
+static PyObject *__Pyx__ImportDottedModule_Error(PyObject *name, PyObject *parts_tuple, Py_ssize_t count) {
+    PyObject *partial_name = NULL, *slice = NULL, *sep = NULL;
+    if (unlikely(PyErr_Occurred())) {
+        PyErr_Clear();
+    }
+    if (likely(PyTuple_GET_SIZE(parts_tuple) == count)) {
+        partial_name = name;
+    } else {
+        slice = PySequence_GetSlice(parts_tuple, 0, count);
+        if (unlikely(!slice))
+            goto bad;
+        sep = PyUnicode_FromStringAndSize(".", 1);
+        if (unlikely(!sep))
+            goto bad;
+        partial_name = PyUnicode_Join(sep, slice);
+    }
+    PyErr_Format(
+#if PY_MAJOR_VERSION < 3
+        PyExc_ImportError,
+        "No module named '%s'", PyString_AS_STRING(partial_name));
+#else
+#if PY_VERSION_HEX >= 0x030600B1
+        PyExc_ModuleNotFoundError,
+#else
+        PyExc_ImportError,
+#endif
+        "No module named '%U'", partial_name);
+#endif
+bad:
+    Py_XDECREF(sep);
+    Py_XDECREF(slice);
+    Py_XDECREF(partial_name);
+    return NULL;
+}
+#endif
+#if PY_MAJOR_VERSION >= 3
+static PyObject *__Pyx__ImportDottedModule_Lookup(PyObject *name) {
+    PyObject *imported_module;
+#if PY_VERSION_HEX < 0x030700A1 || (CYTHON_COMPILING_IN_PYPY && PYPY_VERSION_NUM  < 0x07030400)
+    PyObject *modules = PyImport_GetModuleDict();
+    if (unlikely(!modules))
+        return NULL;
+    imported_module = __Pyx_PyDict_GetItemStr(modules, name);
+    Py_XINCREF(imported_module);
+#else
+    imported_module = PyImport_GetModule(name);
+#endif
+    return imported_module;
+}
+#endif
+#if PY_MAJOR_VERSION >= 3
+static PyObject *__Pyx_ImportDottedModule_WalkParts(PyObject *module, PyObject *name, PyObject *parts_tuple) {
+    Py_ssize_t i, nparts;
+    nparts = PyTuple_GET_SIZE(parts_tuple);
+    for (i=1; i < nparts && module; i++) {
+        PyObject *part, *submodule;
+#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+        part = PyTuple_GET_ITEM(parts_tuple, i);
+#else
+        part = PySequence_ITEM(parts_tuple, i);
+#endif
+        submodule = __Pyx_PyObject_GetAttrStrNoError(module, part);
+#if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
+        Py_DECREF(part);
+#endif
+        Py_DECREF(module);
+        module = submodule;
+    }
+    if (unlikely(!module)) {
+        return __Pyx__ImportDottedModule_Error(name, parts_tuple, i);
+    }
+    return module;
+}
+#endif
+static PyObject *__Pyx__ImportDottedModule(PyObject *name, PyObject *parts_tuple) {
+#if PY_MAJOR_VERSION < 3
+    PyObject *module, *from_list, *star = __pyx_n_s__3;
+    CYTHON_UNUSED_VAR(parts_tuple);
+    from_list = PyList_New(1);
+    if (unlikely(!from_list))
+        return NULL;
+    Py_INCREF(star);
+    PyList_SET_ITEM(from_list, 0, star);
+    module = __Pyx_Import(name, from_list, 0);
+    Py_DECREF(from_list);
+    return module;
+#else
+    PyObject *imported_module;
+    PyObject *module = __Pyx_Import(name, NULL, 0);
+    if (!parts_tuple || unlikely(!module))
+        return module;
+    imported_module = __Pyx__ImportDottedModule_Lookup(name);
+    if (likely(imported_module)) {
+        Py_DECREF(module);
+        return imported_module;
+    }
+    PyErr_Clear();
+    return __Pyx_ImportDottedModule_WalkParts(module, name, parts_tuple);
+#endif
+}
+static PyObject *__Pyx_ImportDottedModule(PyObject *name, PyObject *parts_tuple) {
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030400B1
+    PyObject *module = __Pyx__ImportDottedModule_Lookup(name);
+    if (likely(module)) {
+        PyObject *spec = __Pyx_PyObject_GetAttrStrNoError(module, __pyx_n_s_spec);
+        if (likely(spec)) {
+            PyObject *unsafe = __Pyx_PyObject_GetAttrStrNoError(spec, __pyx_n_s_initializing);
+            if (likely(!unsafe || !__Pyx_PyObject_IsTrue(unsafe))) {
+                Py_DECREF(spec);
+                spec = NULL;
+            }
+            Py_XDECREF(unsafe);
+        }
+        if (likely(!spec)) {
+            PyErr_Clear();
+            return module;
+        }
+        Py_DECREF(spec);
+        Py_DECREF(module);
+    } else if (PyErr_Occurred()) {
+        PyErr_Clear();
+    }
+#endif
+    return __Pyx__ImportDottedModule(name, parts_tuple);
+}
+
+/* FixUpExtensionType */
+  #if CYTHON_USE_TYPE_SPECS
+static int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type) {
+#if PY_VERSION_HEX > 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
+    CYTHON_UNUSED_VAR(spec);
+    CYTHON_UNUSED_VAR(type);
+#else
+    const PyType_Slot *slot = spec->slots;
+    while (slot && slot->slot && slot->slot != Py_tp_members)
+        slot++;
+    if (slot && slot->slot == Py_tp_members) {
+        int changed = 0;
+#if !(PY_VERSION_HEX <= 0x030900b1 && CYTHON_COMPILING_IN_CPYTHON)
+        const
+#endif
+            PyMemberDef *memb = (PyMemberDef*) slot->pfunc;
+        while (memb && memb->name) {
+            if (memb->name[0] == '_' && memb->name[1] == '_') {
+#if PY_VERSION_HEX < 0x030900b1
+                if (strcmp(memb->name, "__weaklistoffset__") == 0) {
+                    assert(memb->type == T_PYSSIZET);
+                    assert(memb->flags == READONLY);
+                    type->tp_weaklistoffset = memb->offset;
+                    changed = 1;
+                }
+                else if (strcmp(memb->name, "__dictoffset__") == 0) {
+                    assert(memb->type == T_PYSSIZET);
+                    assert(memb->flags == READONLY);
+                    type->tp_dictoffset = memb->offset;
+                    changed = 1;
+                }
+#if CYTHON_METH_FASTCALL
+                else if (strcmp(memb->name, "__vectorcalloffset__") == 0) {
+                    assert(memb->type == T_PYSSIZET);
+                    assert(memb->flags == READONLY);
+#if PY_VERSION_HEX >= 0x030800b4
+                    type->tp_vectorcall_offset = memb->offset;
+#else
+                    type->tp_print = (printfunc) memb->offset;
+#endif
+                    changed = 1;
+                }
+#endif
+#else
+                if ((0));
+#endif
+#if PY_VERSION_HEX <= 0x030900b1 && CYTHON_COMPILING_IN_CPYTHON
+                else if (strcmp(memb->name, "__module__") == 0) {
+                    PyObject *descr;
+                    assert(memb->type == T_OBJECT);
+                    assert(memb->flags == 0 || memb->flags == READONLY);
+                    descr = PyDescr_NewMember(type, memb);
+                    if (unlikely(!descr))
+                        return -1;
+                    if (unlikely(PyDict_SetItem(type->tp_dict, PyDescr_NAME(descr), descr) < 0)) {
+                        Py_DECREF(descr);
+                        return -1;
+                    }
+                    Py_DECREF(descr);
+                    changed = 1;
+                }
+#endif
+            }
+            memb++;
+        }
+        if (changed)
+            PyType_Modified(type);
+    }
+#endif
+    return 0;
+}
+#endif
+
+/* FetchSharedCythonModule */
+  static PyObject *__Pyx_FetchSharedCythonABIModule(void) {
+    return __Pyx_PyImport_AddModuleRef((char*) __PYX_ABI_MODULE_NAME);
+}
+
+/* FetchCommonType */
+  static int __Pyx_VerifyCachedType(PyObject *cached_type,
+                               const char *name,
+                               Py_ssize_t basicsize,
+                               Py_ssize_t expected_basicsize) {
+    if (!PyType_Check(cached_type)) {
+        PyErr_Format(PyExc_TypeError,
+            "Shared Cython type %.200s is not a type object", name);
+        return -1;
+    }
+    if (basicsize != expected_basicsize) {
+        PyErr_Format(PyExc_TypeError,
+            "Shared Cython type %.200s has the wrong size, try recompiling",
+            name);
+        return -1;
+    }
+    return 0;
+}
+#if !CYTHON_USE_TYPE_SPECS
+static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
+    PyObject* abi_module;
+    const char* object_name;
+    PyTypeObject *cached_type = NULL;
+    abi_module = __Pyx_FetchSharedCythonABIModule();
+    if (!abi_module) return NULL;
+    object_name = strrchr(type->tp_name, '.');
+    object_name = object_name ? object_name+1 : type->tp_name;
+    cached_type = (PyTypeObject*) PyObject_GetAttrString(abi_module, object_name);
+    if (cached_type) {
+        if (__Pyx_VerifyCachedType(
+              (PyObject *)cached_type,
+              object_name,
+              cached_type->tp_basicsize,
+              type->tp_basicsize) < 0) {
+            goto bad;
+        }
+        goto done;
+    }
+    if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
+    PyErr_Clear();
+    if (PyType_Ready(type) < 0) goto bad;
+    if (PyObject_SetAttrString(abi_module, object_name, (PyObject *)type) < 0)
+        goto bad;
+    Py_INCREF(type);
+    cached_type = type;
+done:
+    Py_DECREF(abi_module);
+    return cached_type;
+bad:
+    Py_XDECREF(cached_type);
+    cached_type = NULL;
+    goto done;
+}
+#else
+static PyTypeObject *__Pyx_FetchCommonTypeFromSpec(PyObject *module, PyType_Spec *spec, PyObject *bases) {
+    PyObject *abi_module, *cached_type = NULL;
+    const char* object_name = strrchr(spec->name, '.');
+    object_name = object_name ? object_name+1 : spec->name;
+    abi_module = __Pyx_FetchSharedCythonABIModule();
+    if (!abi_module) return NULL;
+    cached_type = PyObject_GetAttrString(abi_module, object_name);
+    if (cached_type) {
+        Py_ssize_t basicsize;
+#if CYTHON_COMPILING_IN_LIMITED_API
+        PyObject *py_basicsize;
+        py_basicsize = PyObject_GetAttrString(cached_type, "__basicsize__");
+        if (unlikely(!py_basicsize)) goto bad;
+        basicsize = PyLong_AsSsize_t(py_basicsize);
+        Py_DECREF(py_basicsize);
+        py_basicsize = 0;
+        if (unlikely(basicsize == (Py_ssize_t)-1) && PyErr_Occurred()) goto bad;
+#else
+        basicsize = likely(PyType_Check(cached_type)) ? ((PyTypeObject*) cached_type)->tp_basicsize : -1;
+#endif
+        if (__Pyx_VerifyCachedType(
+              cached_type,
+              object_name,
+              basicsize,
+              spec->basicsize) < 0) {
+            goto bad;
+        }
+        goto done;
+    }
+    if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
+    PyErr_Clear();
+    CYTHON_UNUSED_VAR(module);
+    cached_type = __Pyx_PyType_FromModuleAndSpec(abi_module, spec, bases);
+    if (unlikely(!cached_type)) goto bad;
+    if (unlikely(__Pyx_fix_up_extension_type_from_spec(spec, (PyTypeObject *) cached_type) < 0)) goto bad;
+    if (PyObject_SetAttrString(abi_module, object_name, cached_type) < 0) goto bad;
+done:
+    Py_DECREF(abi_module);
+    assert(cached_type == NULL || PyType_Check(cached_type));
+    return (PyTypeObject *) cached_type;
+bad:
+    Py_XDECREF(cached_type);
+    cached_type = NULL;
+    goto done;
+}
+#endif
+
+/* PyVectorcallFastCallDict */
+  #if CYTHON_METH_FASTCALL
+static PyObject *__Pyx_PyVectorcall_FastCallDict_kw(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw)
+{
+    PyObject *res = NULL;
+    PyObject *kwnames;
+    PyObject **newargs;
+    PyObject **kwvalues;
+    Py_ssize_t i, pos;
+    size_t j;
+    PyObject *key, *value;
+    unsigned long keys_are_strings;
+    Py_ssize_t nkw = PyDict_GET_SIZE(kw);
+    newargs = (PyObject **)PyMem_Malloc((nargs + (size_t)nkw) * sizeof(args[0]));
+    if (unlikely(newargs == NULL)) {
+        PyErr_NoMemory();
+        return NULL;
+    }
+    for (j = 0; j < nargs; j++) newargs[j] = args[j];
+    kwnames = PyTuple_New(nkw);
+    if (unlikely(kwnames == NULL)) {
+        PyMem_Free(newargs);
+        return NULL;
+    }
+    kwvalues = newargs + nargs;
+    pos = i = 0;
+    keys_are_strings = Py_TPFLAGS_UNICODE_SUBCLASS;
+    while (PyDict_Next(kw, &pos, &key, &value)) {
+        keys_are_strings &= Py_TYPE(key)->tp_flags;
+        Py_INCREF(key);
+        Py_INCREF(value);
+        PyTuple_SET_ITEM(kwnames, i, key);
+        kwvalues[i] = value;
+        i++;
+    }
+    if (unlikely(!keys_are_strings)) {
+        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
+        goto cleanup;
+    }
+    res = vc(func, newargs, nargs, kwnames);
+cleanup:
+    Py_DECREF(kwnames);
+    for (i = 0; i < nkw; i++)
+        Py_DECREF(kwvalues[i]);
+    PyMem_Free(newargs);
+    return res;
+}
+static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw)
+{
+    if (likely(kw == NULL) || PyDict_GET_SIZE(kw) == 0) {
+        return vc(func, args, nargs, NULL);
+    }
+    return __Pyx_PyVectorcall_FastCallDict_kw(func, vc, args, nargs, kw);
+}
+#endif
+
+/* CythonFunctionShared */
+  #if CYTHON_COMPILING_IN_LIMITED_API
+static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void *cfunc) {
+    if (__Pyx_CyFunction_Check(func)) {
+        return PyCFunction_GetFunction(((__pyx_CyFunctionObject*)func)->func) == (PyCFunction) cfunc;
+    } else if (PyCFunction_Check(func)) {
+        return PyCFunction_GetFunction(func) == (PyCFunction) cfunc;
+    }
+    return 0;
+}
+#else
+static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void *cfunc) {
+    return __Pyx_CyOrPyCFunction_Check(func) && __Pyx_CyOrPyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc;
+}
+#endif
+static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj) {
+#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
+    __Pyx_Py_XDECREF_SET(
+        __Pyx_CyFunction_GetClassObj(f),
+            ((classobj) ? __Pyx_NewRef(classobj) : NULL));
+#else
+    __Pyx_Py_XDECREF_SET(
+        ((PyCMethodObject *) (f))->mm_class,
+        (PyTypeObject*)((classobj) ? __Pyx_NewRef(classobj) : NULL));
+#endif
+}
+static PyObject *
+__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, void *closure)
+{
+    CYTHON_UNUSED_VAR(closure);
+    if (unlikely(op->func_doc == NULL)) {
+#if CYTHON_COMPILING_IN_LIMITED_API
+        op->func_doc = PyObject_GetAttrString(op->func, "__doc__");
+        if (unlikely(!op->func_doc)) return NULL;
+#else
+        if (((PyCFunctionObject*)op)->m_ml->ml_doc) {
+#if PY_MAJOR_VERSION >= 3
+            op->func_doc = PyUnicode_FromString(((PyCFunctionObject*)op)->m_ml->ml_doc);
+#else
+            op->func_doc = PyString_FromString(((PyCFunctionObject*)op)->m_ml->ml_doc);
+#endif
+            if (unlikely(op->func_doc == NULL))
+                return NULL;
+        } else {
+            Py_INCREF(Py_None);
+            return Py_None;
+        }
+#endif
+    }
+    Py_INCREF(op->func_doc);
+    return op->func_doc;
+}
+static int
+__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+    if (value == NULL) {
+        value = Py_None;
+    }
+    Py_INCREF(value);
+    __Pyx_Py_XDECREF_SET(op->func_doc, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+    if (unlikely(op->func_name == NULL)) {
+#if CYTHON_COMPILING_IN_LIMITED_API
+        op->func_name = PyObject_GetAttrString(op->func, "__name__");
+#elif PY_MAJOR_VERSION >= 3
+        op->func_name = PyUnicode_InternFromString(((PyCFunctionObject*)op)->m_ml->ml_name);
+#else
+        op->func_name = PyString_InternFromString(((PyCFunctionObject*)op)->m_ml->ml_name);
+#endif
+        if (unlikely(op->func_name == NULL))
+            return NULL;
+    }
+    Py_INCREF(op->func_name);
+    return op->func_name;
+}
+static int
+__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+#if PY_MAJOR_VERSION >= 3
+    if (unlikely(value == NULL || !PyUnicode_Check(value)))
+#else
+    if (unlikely(value == NULL || !PyString_Check(value)))
+#endif
+    {
+        PyErr_SetString(PyExc_TypeError,
+                        "__name__ must be set to a string object");
+        return -1;
+    }
+    Py_INCREF(value);
+    __Pyx_Py_XDECREF_SET(op->func_name, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+    Py_INCREF(op->func_qualname);
+    return op->func_qualname;
+}
+static int
+__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+#if PY_MAJOR_VERSION >= 3
+    if (unlikely(value == NULL || !PyUnicode_Check(value)))
+#else
+    if (unlikely(value == NULL || !PyString_Check(value)))
+#endif
+    {
+        PyErr_SetString(PyExc_TypeError,
+                        "__qualname__ must be set to a string object");
+        return -1;
+    }
+    Py_INCREF(value);
+    __Pyx_Py_XDECREF_SET(op->func_qualname, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+    if (unlikely(op->func_dict == NULL)) {
+        op->func_dict = PyDict_New();
+        if (unlikely(op->func_dict == NULL))
+            return NULL;
+    }
+    Py_INCREF(op->func_dict);
+    return op->func_dict;
+}
+static int
+__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+    if (unlikely(value == NULL)) {
+        PyErr_SetString(PyExc_TypeError,
+               "function's dictionary may not be deleted");
+        return -1;
+    }
+    if (unlikely(!PyDict_Check(value))) {
+        PyErr_SetString(PyExc_TypeError,
+               "setting function's dictionary to a non-dict");
+        return -1;
+    }
+    Py_INCREF(value);
+    __Pyx_Py_XDECREF_SET(op->func_dict, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op, void *context)
+{
+    CYTHON_UNUSED_VAR(context);
+    Py_INCREF(op->func_globals);
+    return op->func_globals;
+}
+static PyObject *
+__Pyx_CyFunction_get_closure(__pyx_CyFunctionObject *op, void *context)
+{
+    CYTHON_UNUSED_VAR(op);
+    CYTHON_UNUSED_VAR(context);
+    Py_INCREF(Py_None);
+    return Py_None;
+}
+static PyObject *
+__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op, void *context)
+{
+    PyObject* result = (op->func_code) ? op->func_code : Py_None;
+    CYTHON_UNUSED_VAR(context);
+    Py_INCREF(result);
+    return result;
+}
+static int
+__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) {
+    int result = 0;
+    PyObject *res = op->defaults_getter((PyObject *) op);
+    if (unlikely(!res))
+        return -1;
+    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+    op->defaults_tuple = PyTuple_GET_ITEM(res, 0);
+    Py_INCREF(op->defaults_tuple);
+    op->defaults_kwdict = PyTuple_GET_ITEM(res, 1);
+    Py_INCREF(op->defaults_kwdict);
+    #else
+    op->defaults_tuple = __Pyx_PySequence_ITEM(res, 0);
+    if (unlikely(!op->defaults_tuple)) result = -1;
+    else {
+        op->defaults_kwdict = __Pyx_PySequence_ITEM(res, 1);
+        if (unlikely(!op->defaults_kwdict)) result = -1;
+    }
+    #endif
+    Py_DECREF(res);
+    return result;
+}
+static int
+__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
+    CYTHON_UNUSED_VAR(context);
+    if (!value) {
+        value = Py_None;
+    } else if (unlikely(value != Py_None && !PyTuple_Check(value))) {
+        PyErr_SetString(PyExc_TypeError,
+                        "__defaults__ must be set to a tuple object");
+        return -1;
+    }
+    PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__defaults__ will not "
+                 "currently affect the values used in function calls", 1);
+    Py_INCREF(value);
+    __Pyx_Py_XDECREF_SET(op->defaults_tuple, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op, void *context) {
+    PyObject* result = op->defaults_tuple;
+    CYTHON_UNUSED_VAR(context);
+    if (unlikely(!result)) {
+        if (op->defaults_getter) {
+            if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL;
+            result = op->defaults_tuple;
+        } else {
+            result = Py_None;
+        }
+    }
+    Py_INCREF(result);
+    return result;
+}
+static int
+__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
+    CYTHON_UNUSED_VAR(context);
+    if (!value) {
+        value = Py_None;
+    } else if (unlikely(value != Py_None && !PyDict_Check(value))) {
+        PyErr_SetString(PyExc_TypeError,
+                        "__kwdefaults__ must be set to a dict object");
+        return -1;
+    }
+    PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__kwdefaults__ will not "
+                 "currently affect the values used in function calls", 1);
+    Py_INCREF(value);
+    __Pyx_Py_XDECREF_SET(op->defaults_kwdict, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op, void *context) {
+    PyObject* result = op->defaults_kwdict;
+    CYTHON_UNUSED_VAR(context);
+    if (unlikely(!result)) {
+        if (op->defaults_getter) {
+            if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL;
+            result = op->defaults_kwdict;
+        } else {
+            result = Py_None;
+        }
+    }
+    Py_INCREF(result);
+    return result;
+}
+static int
+__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
+    CYTHON_UNUSED_VAR(context);
+    if (!value || value == Py_None) {
+        value = NULL;
+    } else if (unlikely(!PyDict_Check(value))) {
+        PyErr_SetString(PyExc_TypeError,
+                        "__annotations__ must be set to a dict object");
+        return -1;
+    }
+    Py_XINCREF(value);
+    __Pyx_Py_XDECREF_SET(op->func_annotations, value);
+    return 0;
+}
+static PyObject *
+__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op, void *context) {
+    PyObject* result = op->func_annotations;
+    CYTHON_UNUSED_VAR(context);
+    if (unlikely(!result)) {
+        result = PyDict_New();
+        if (unlikely(!result)) return NULL;
+        op->func_annotations = result;
+    }
+    Py_INCREF(result);
+    return result;
+}
+static PyObject *
+__Pyx_CyFunction_get_is_coroutine(__pyx_CyFunctionObject *op, void *context) {
+    int is_coroutine;
+    CYTHON_UNUSED_VAR(context);
+    if (op->func_is_coroutine) {
+        return __Pyx_NewRef(op->func_is_coroutine);
+    }
+    is_coroutine = op->flags & __Pyx_CYFUNCTION_COROUTINE;
+#if PY_VERSION_HEX >= 0x03050000
+    if (is_coroutine) {
+        PyObject *module, *fromlist, *marker = __pyx_n_s_is_coroutine;
+        fromlist = PyList_New(1);
+        if (unlikely(!fromlist)) return NULL;
+        Py_INCREF(marker);
+#if CYTHON_ASSUME_SAFE_MACROS
+        PyList_SET_ITEM(fromlist, 0, marker);
+#else
+        if (unlikely(PyList_SetItem(fromlist, 0, marker) < 0)) {
+            Py_DECREF(marker);
+            Py_DECREF(fromlist);
+            return NULL;
+        }
+#endif
+        module = PyImport_ImportModuleLevelObject(__pyx_n_s_asyncio_coroutines, NULL, NULL, fromlist, 0);
+        Py_DECREF(fromlist);
+        if (unlikely(!module)) goto ignore;
+        op->func_is_coroutine = __Pyx_PyObject_GetAttrStr(module, marker);
+        Py_DECREF(module);
+        if (likely(op->func_is_coroutine)) {
+            return __Pyx_NewRef(op->func_is_coroutine);
+        }
+ignore:
+        PyErr_Clear();
+    }
+#endif
+    op->func_is_coroutine = __Pyx_PyBool_FromLong(is_coroutine);
+    return __Pyx_NewRef(op->func_is_coroutine);
+}
+#if CYTHON_COMPILING_IN_LIMITED_API
+static PyObject *
+__Pyx_CyFunction_get_module(__pyx_CyFunctionObject *op, void *context) {
+    CYTHON_UNUSED_VAR(context);
+    return PyObject_GetAttrString(op->func, "__module__");
+}
+static int
+__Pyx_CyFunction_set_module(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
+    CYTHON_UNUSED_VAR(context);
+    return PyObject_SetAttrString(op->func, "__module__", value);
+}
+#endif
+static PyGetSetDef __pyx_CyFunction_getsets[] = {
+    {(char *) "func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
+    {(char *) "__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
+    {(char *) "func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
+    {(char *) "__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
+    {(char *) "__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0},
+    {(char *) "func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
+    {(char *) "__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
+    {(char *) "func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
+    {(char *) "__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
+    {(char *) "func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
+    {(char *) "__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
+    {(char *) "func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
+    {(char *) "__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
+    {(char *) "func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
+    {(char *) "__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
+    {(char *) "__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0},
+    {(char *) "__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0},
+    {(char *) "_is_coroutine", (getter)__Pyx_CyFunction_get_is_coroutine, 0, 0, 0},
+#if CYTHON_COMPILING_IN_LIMITED_API
+    {"__module__", (getter)__Pyx_CyFunction_get_module, (setter)__Pyx_CyFunction_set_module, 0, 0},
+#endif
+    {0, 0, 0, 0, 0}
+};
+static PyMemberDef __pyx_CyFunction_members[] = {
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    {(char *) "__module__", T_OBJECT, offsetof(PyCFunctionObject, m_module), 0, 0},
+#endif
+#if CYTHON_USE_TYPE_SPECS
+    {(char *) "__dictoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_dict), READONLY, 0},
+#if CYTHON_METH_FASTCALL
+#if CYTHON_BACKPORT_VECTORCALL
+    {(char *) "__vectorcalloffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_vectorcall), READONLY, 0},
+#else
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    {(char *) "__vectorcalloffset__", T_PYSSIZET, offsetof(PyCFunctionObject, vectorcall), READONLY, 0},
+#endif
+#endif
+#endif
+#if PY_VERSION_HEX < 0x030500A0 || CYTHON_COMPILING_IN_LIMITED_API
+    {(char *) "__weaklistoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_weakreflist), READONLY, 0},
+#else
+    {(char *) "__weaklistoffset__", T_PYSSIZET, offsetof(PyCFunctionObject, m_weakreflist), READONLY, 0},
+#endif
+#endif
+    {0, 0, 0,  0, 0}
+};
+static PyObject *
+__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, PyObject *args)
+{
+    CYTHON_UNUSED_VAR(args);
+#if PY_MAJOR_VERSION >= 3
+    Py_INCREF(m->func_qualname);
+    return m->func_qualname;
+#else
+    return PyString_FromString(((PyCFunctionObject*)m)->m_ml->ml_name);
+#endif
+}
+static PyMethodDef __pyx_CyFunction_methods[] = {
+    {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
+    {0, 0, 0, 0}
+};
+#if PY_VERSION_HEX < 0x030500A0 || CYTHON_COMPILING_IN_LIMITED_API
+#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
+#else
+#define __Pyx_CyFunction_weakreflist(cyfunc) (((PyCFunctionObject*)cyfunc)->m_weakreflist)
+#endif
+static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject *op, PyMethodDef *ml, int flags, PyObject* qualname,
+                                       PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    PyCFunctionObject *cf = (PyCFunctionObject*) op;
+#endif
+    if (unlikely(op == NULL))
+        return NULL;
+#if CYTHON_COMPILING_IN_LIMITED_API
+    op->func = PyCFunction_NewEx(ml, (PyObject*)op, module);
+    if (unlikely(!op->func)) return NULL;
+#endif
+    op->flags = flags;
+    __Pyx_CyFunction_weakreflist(op) = NULL;
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    cf->m_ml = ml;
+    cf->m_self = (PyObject *) op;
+#endif
+    Py_XINCREF(closure);
+    op->func_closure = closure;
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    Py_XINCREF(module);
+    cf->m_module = module;
+#endif
+    op->func_dict = NULL;
+    op->func_name = NULL;
+    Py_INCREF(qualname);
+    op->func_qualname = qualname;
+    op->func_doc = NULL;
+#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
+    op->func_classobj = NULL;
+#else
+    ((PyCMethodObject*)op)->mm_class = NULL;
+#endif
+    op->func_globals = globals;
+    Py_INCREF(op->func_globals);
+    Py_XINCREF(code);
+    op->func_code = code;
+    op->defaults_pyobjects = 0;
+    op->defaults_size = 0;
+    op->defaults = NULL;
+    op->defaults_tuple = NULL;
+    op->defaults_kwdict = NULL;
+    op->defaults_getter = NULL;
+    op->func_annotations = NULL;
+    op->func_is_coroutine = NULL;
+#if CYTHON_METH_FASTCALL
+    switch (ml->ml_flags & (METH_VARARGS | METH_FASTCALL | METH_NOARGS | METH_O | METH_KEYWORDS | METH_METHOD)) {
+    case METH_NOARGS:
+        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_NOARGS;
+        break;
+    case METH_O:
+        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_O;
+        break;
+    case METH_METHOD | METH_FASTCALL | METH_KEYWORDS:
+        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD;
+        break;
+    case METH_FASTCALL | METH_KEYWORDS:
+        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS;
+        break;
+    case METH_VARARGS | METH_KEYWORDS:
+        __Pyx_CyFunction_func_vectorcall(op) = NULL;
+        break;
+    default:
+        PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction");
+        Py_DECREF(op);
+        return NULL;
+    }
+#endif
+    return (PyObject *) op;
+}
+static int
+__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
+{
+    Py_CLEAR(m->func_closure);
+#if CYTHON_COMPILING_IN_LIMITED_API
+    Py_CLEAR(m->func);
+#else
+    Py_CLEAR(((PyCFunctionObject*)m)->m_module);
+#endif
+    Py_CLEAR(m->func_dict);
+    Py_CLEAR(m->func_name);
+    Py_CLEAR(m->func_qualname);
+    Py_CLEAR(m->func_doc);
+    Py_CLEAR(m->func_globals);
+    Py_CLEAR(m->func_code);
+#if !CYTHON_COMPILING_IN_LIMITED_API
+#if PY_VERSION_HEX < 0x030900B1
+    Py_CLEAR(__Pyx_CyFunction_GetClassObj(m));
+#else
+    {
+        PyObject *cls = (PyObject*) ((PyCMethodObject *) (m))->mm_class;
+        ((PyCMethodObject *) (m))->mm_class = NULL;
+        Py_XDECREF(cls);
+    }
+#endif
+#endif
+    Py_CLEAR(m->defaults_tuple);
+    Py_CLEAR(m->defaults_kwdict);
+    Py_CLEAR(m->func_annotations);
+    Py_CLEAR(m->func_is_coroutine);
+    if (m->defaults) {
+        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
+        int i;
+        for (i = 0; i < m->defaults_pyobjects; i++)
+            Py_XDECREF(pydefaults[i]);
+        PyObject_Free(m->defaults);
+        m->defaults = NULL;
+    }
+    return 0;
+}
+static void __Pyx__CyFunction_dealloc(__pyx_CyFunctionObject *m)
+{
+    if (__Pyx_CyFunction_weakreflist(m) != NULL)
+        PyObject_ClearWeakRefs((PyObject *) m);
+    __Pyx_CyFunction_clear(m);
+    __Pyx_PyHeapTypeObject_GC_Del(m);
+}
+static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
+{
+    PyObject_GC_UnTrack(m);
+    __Pyx__CyFunction_dealloc(m);
+}
+static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
+{
+    Py_VISIT(m->func_closure);
+#if CYTHON_COMPILING_IN_LIMITED_API
+    Py_VISIT(m->func);
+#else
+    Py_VISIT(((PyCFunctionObject*)m)->m_module);
+#endif
+    Py_VISIT(m->func_dict);
+    Py_VISIT(m->func_name);
+    Py_VISIT(m->func_qualname);
+    Py_VISIT(m->func_doc);
+    Py_VISIT(m->func_globals);
+    Py_VISIT(m->func_code);
+#if !CYTHON_COMPILING_IN_LIMITED_API
+    Py_VISIT(__Pyx_CyFunction_GetClassObj(m));
+#endif
+    Py_VISIT(m->defaults_tuple);
+    Py_VISIT(m->defaults_kwdict);
+    Py_VISIT(m->func_is_coroutine);
+    if (m->defaults) {
+        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
+        int i;
+        for (i = 0; i < m->defaults_pyobjects; i++)
+            Py_VISIT(pydefaults[i]);
+    }
+    return 0;
+}
+static PyObject*
+__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
+{
+#if PY_MAJOR_VERSION >= 3
+    return PyUnicode_FromFormat("<cyfunction %U at %p>",
+                                op->func_qualname, (void *)op);
+#else
+    return PyString_FromFormat("<cyfunction %s at %p>",
+                               PyString_AsString(op->func_qualname), (void *)op);
+#endif
+}
+static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) {
+#if CYTHON_COMPILING_IN_LIMITED_API
+    PyObject *f = ((__pyx_CyFunctionObject*)func)->func;
+    PyObject *py_name = NULL;
+    PyCFunction meth;
+    int flags;
+    meth = PyCFunction_GetFunction(f);
+    if (unlikely(!meth)) return NULL;
+    flags = PyCFunction_GetFlags(f);
+    if (unlikely(flags < 0)) return NULL;
+#else
+    PyCFunctionObject* f = (PyCFunctionObject*)func;
+    PyCFunction meth = f->m_ml->ml_meth;
+    int flags = f->m_ml->ml_flags;
+#endif
+    Py_ssize_t size;
+    switch (flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) {
+    case METH_VARARGS:
+        if (likely(kw == NULL || PyDict_Size(kw) == 0))
+            return (*meth)(self, arg);
+        break;
+    case METH_VARARGS | METH_KEYWORDS:
+        return (*(PyCFunctionWithKeywords)(void*)meth)(self, arg, kw);
+    case METH_NOARGS:
+        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
+#if CYTHON_ASSUME_SAFE_MACROS
+            size = PyTuple_GET_SIZE(arg);
+#else
+            size = PyTuple_Size(arg);
+            if (unlikely(size < 0)) return NULL;
+#endif
+            if (likely(size == 0))
+                return (*meth)(self, NULL);
+#if CYTHON_COMPILING_IN_LIMITED_API
+            py_name = __Pyx_CyFunction_get_name((__pyx_CyFunctionObject*)func, NULL);
+            if (!py_name) return NULL;
+            PyErr_Format(PyExc_TypeError,
+                "%.200S() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                py_name, size);
+            Py_DECREF(py_name);
+#else
+            PyErr_Format(PyExc_TypeError,
+                "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                f->m_ml->ml_name, size);
+#endif
+            return NULL;
+        }
+        break;
+    case METH_O:
+        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
+#if CYTHON_ASSUME_SAFE_MACROS
+            size = PyTuple_GET_SIZE(arg);
+#else
+            size = PyTuple_Size(arg);
+            if (unlikely(size < 0)) return NULL;
+#endif
+            if (likely(size == 1)) {
+                PyObject *result, *arg0;
+                #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
+                arg0 = PyTuple_GET_ITEM(arg, 0);
+                #else
+                arg0 = __Pyx_PySequence_ITEM(arg, 0); if (unlikely(!arg0)) return NULL;
+                #endif
+                result = (*meth)(self, arg0);
+                #if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
+                Py_DECREF(arg0);
+                #endif
+                return result;
+            }
+#if CYTHON_COMPILING_IN_LIMITED_API
+            py_name = __Pyx_CyFunction_get_name((__pyx_CyFunctionObject*)func, NULL);
+            if (!py_name) return NULL;
+            PyErr_Format(PyExc_TypeError,
+                "%.200S() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                py_name, size);
+            Py_DECREF(py_name);
+#else
+            PyErr_Format(PyExc_TypeError,
+                "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
+                f->m_ml->ml_name, size);
+#endif
+            return NULL;
+        }
+        break;
+    default:
+        PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction");
+        return NULL;
+    }
+#if CYTHON_COMPILING_IN_LIMITED_API
+    py_name = __Pyx_CyFunction_get_name((__pyx_CyFunctionObject*)func, NULL);
+    if (!py_name) return NULL;
+    PyErr_Format(PyExc_TypeError, "%.200S() takes no keyword arguments",
+                 py_name);
+    Py_DECREF(py_name);
+#else
+    PyErr_Format(PyExc_TypeError, "%.200s() takes no keyword arguments",
+                 f->m_ml->ml_name);
+#endif
+    return NULL;
+}
+static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
+    PyObject *self, *result;
+#if CYTHON_COMPILING_IN_LIMITED_API
+    self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)func)->func);
+    if (unlikely(!self) && PyErr_Occurred()) return NULL;
+#else
+    self = ((PyCFunctionObject*)func)->m_self;
+#endif
+    result = __Pyx_CyFunction_CallMethod(func, self, arg, kw);
+    return result;
+}
+static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) {
+    PyObject *result;
+    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func;
+#if CYTHON_METH_FASTCALL
+     __pyx_vectorcallfunc vc = __Pyx_CyFunction_func_vectorcall(cyfunc);
+    if (vc) {
+#if CYTHON_ASSUME_SAFE_MACROS
+        return __Pyx_PyVectorcall_FastCallDict(func, vc, &PyTuple_GET_ITEM(args, 0), (size_t)PyTuple_GET_SIZE(args), kw);
+#else
+        (void) &__Pyx_PyVectorcall_FastCallDict;
+        return PyVectorcall_Call(func, args, kw);
+#endif
+    }
+#endif
+    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
+        Py_ssize_t argc;
+        PyObject *new_args;
+        PyObject *self;
+#if CYTHON_ASSUME_SAFE_MACROS
+        argc = PyTuple_GET_SIZE(args);
+#else
+        argc = PyTuple_Size(args);
+        if (unlikely(!argc) < 0) return NULL;
+#endif
+        new_args = PyTuple_GetSlice(args, 1, argc);
+        if (unlikely(!new_args))
+            return NULL;
+        self = PyTuple_GetItem(args, 0);
+        if (unlikely(!self)) {
+            Py_DECREF(new_args);
+#if PY_MAJOR_VERSION > 2
+            PyErr_Format(PyExc_TypeError,
+                         "unbound method %.200S() needs an argument",
+                         cyfunc->func_qualname);
+#else
+            PyErr_SetString(PyExc_TypeError,
+                            "unbound method needs an argument");
+#endif
+            return NULL;
+        }
+        result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw);
+        Py_DECREF(new_args);
+    } else {
+        result = __Pyx_CyFunction_Call(func, args, kw);
+    }
+    return result;
+}
+#if CYTHON_METH_FASTCALL
+static CYTHON_INLINE int __Pyx_CyFunction_Vectorcall_CheckArgs(__pyx_CyFunctionObject *cyfunc, Py_ssize_t nargs, PyObject *kwnames)
+{
+    int ret = 0;
+    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
+        if (unlikely(nargs < 1)) {
+            PyErr_Format(PyExc_TypeError, "%.200s() needs an argument",
+                         ((PyCFunctionObject*)cyfunc)->m_ml->ml_name);
+            return -1;
+        }
+        ret = 1;
+    }
+    if (unlikely(kwnames) && unlikely(PyTuple_GET_SIZE(kwnames))) {
+        PyErr_Format(PyExc_TypeError,
+                     "%.200s() takes no keyword arguments", ((PyCFunctionObject*)cyfunc)->m_ml->ml_name);
+        return -1;
+    }
+    return ret;
+}
+static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
+{
+    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
+    PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml;
+#if CYTHON_BACKPORT_VECTORCALL
+    Py_ssize_t nargs = (Py_ssize_t)nargsf;
+#else
+    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
+#endif
+    PyObject *self;
+    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) {
+    case 1:
+        self = args[0];
+        args += 1;
+        nargs -= 1;
+        break;
+    case 0:
+        self = ((PyCFunctionObject*)cyfunc)->m_self;
+        break;
+    default:
+        return NULL;
+    }
+    if (unlikely(nargs != 0)) {
+        PyErr_Format(PyExc_TypeError,
+            "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
+            def->ml_name, nargs);
+        return NULL;
+    }
+    return def->ml_meth(self, NULL);
+}
+static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
+{
+    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
+    PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml;
+#if CYTHON_BACKPORT_VECTORCALL
+    Py_ssize_t nargs = (Py_ssize_t)nargsf;
+#else
+    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
+#endif
+    PyObject *self;
+    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) {
+    case 1:
+        self = args[0];
+        args += 1;
+        nargs -= 1;
+        break;
+    case 0:
+        self = ((PyCFunctionObject*)cyfunc)->m_self;
+        break;
+    default:
+        return NULL;
+    }
+    if (unlikely(nargs != 1)) {
+        PyErr_Format(PyExc_TypeError,
+            "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
+            def->ml_name, nargs);
+        return NULL;
+    }
+    return def->ml_meth(self, args[0]);
+}
+static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
+{
+    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
+    PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml;
+#if CYTHON_BACKPORT_VECTORCALL
+    Py_ssize_t nargs = (Py_ssize_t)nargsf;
+#else
+    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
+#endif
+    PyObject *self;
+    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) {
+    case 1:
+        self = args[0];
+        args += 1;
+        nargs -= 1;
+        break;
+    case 0:
+        self = ((PyCFunctionObject*)cyfunc)->m_self;
+        break;
+    default:
+        return NULL;
+    }
+    return ((__Pyx_PyCFunctionFastWithKeywords)(void(*)(void))def->ml_meth)(self, args, nargs, kwnames);
+}
+static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
+{
+    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
+    PyMethodDef* def = ((PyCFunctionObject*)cyfunc)->m_ml;
+    PyTypeObject *cls = (PyTypeObject *) __Pyx_CyFunction_GetClassObj(cyfunc);
+#if CYTHON_BACKPORT_VECTORCALL
+    Py_ssize_t nargs = (Py_ssize_t)nargsf;
+#else
+    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
+#endif
+    PyObject *self;
+    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) {
+    case 1:
+        self = args[0];
+        args += 1;
+        nargs -= 1;
+        break;
+    case 0:
+        self = ((PyCFunctionObject*)cyfunc)->m_self;
+        break;
+    default:
+        return NULL;
+    }
+    return ((__Pyx_PyCMethod)(void(*)(void))def->ml_meth)(self, cls, args, (size_t)nargs, kwnames);
+}
+#endif
+#if CYTHON_USE_TYPE_SPECS
+static PyType_Slot __pyx_CyFunctionType_slots[] = {
+    {Py_tp_dealloc, (void *)__Pyx_CyFunction_dealloc},
+    {Py_tp_repr, (void *)__Pyx_CyFunction_repr},
+    {Py_tp_call, (void *)__Pyx_CyFunction_CallAsMethod},
+    {Py_tp_traverse, (void *)__Pyx_CyFunction_traverse},
+    {Py_tp_clear, (void *)__Pyx_CyFunction_clear},
+    {Py_tp_methods, (void *)__pyx_CyFunction_methods},
+    {Py_tp_members, (void *)__pyx_CyFunction_members},
+    {Py_tp_getset, (void *)__pyx_CyFunction_getsets},
+    {Py_tp_descr_get, (void *)__Pyx_PyMethod_New},
+    {0, 0},
+};
+static PyType_Spec __pyx_CyFunctionType_spec = {
+    __PYX_TYPE_MODULE_PREFIX "cython_function_or_method",
+    sizeof(__pyx_CyFunctionObject),
+    0,
+#ifdef Py_TPFLAGS_METHOD_DESCRIPTOR
+    Py_TPFLAGS_METHOD_DESCRIPTOR |
+#endif
+#if (defined(_Py_TPFLAGS_HAVE_VECTORCALL) && CYTHON_METH_FASTCALL)
+    _Py_TPFLAGS_HAVE_VECTORCALL |
+#endif
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_BASETYPE,
+    __pyx_CyFunctionType_slots
+};
+#else
+static PyTypeObject __pyx_CyFunctionType_type = {
+    PyVarObject_HEAD_INIT(0, 0)
+    __PYX_TYPE_MODULE_PREFIX "cython_function_or_method",
+    sizeof(__pyx_CyFunctionObject),
+    0,
+    (destructor) __Pyx_CyFunction_dealloc,
+#if !CYTHON_METH_FASTCALL
+    0,
+#elif CYTHON_BACKPORT_VECTORCALL
+    (printfunc)offsetof(__pyx_CyFunctionObject, func_vectorcall),
+#else
+    offsetof(PyCFunctionObject, vectorcall),
+#endif
+    0,
+    0,
+#if PY_MAJOR_VERSION < 3
+    0,
+#else
+    0,
+#endif
+    (reprfunc) __Pyx_CyFunction_repr,
+    0,
+    0,
+    0,
+    0,
+    __Pyx_CyFunction_CallAsMethod,
+    0,
+    0,
+    0,
+    0,
+#ifdef Py_TPFLAGS_METHOD_DESCRIPTOR
+    Py_TPFLAGS_METHOD_DESCRIPTOR |
+#endif
+#if defined(_Py_TPFLAGS_HAVE_VECTORCALL) && CYTHON_METH_FASTCALL
+    _Py_TPFLAGS_HAVE_VECTORCALL |
+#endif
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_BASETYPE,
+    0,
+    (traverseproc) __Pyx_CyFunction_traverse,
+    (inquiry) __Pyx_CyFunction_clear,
+    0,
+#if PY_VERSION_HEX < 0x030500A0
+    offsetof(__pyx_CyFunctionObject, func_weakreflist),
+#else
+    offsetof(PyCFunctionObject, m_weakreflist),
+#endif
+    0,
+    0,
+    __pyx_CyFunction_methods,
+    __pyx_CyFunction_members,
+    __pyx_CyFunction_getsets,
+    0,
+    0,
+    __Pyx_PyMethod_New,
+    0,
+    offsetof(__pyx_CyFunctionObject, func_dict),
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+#if PY_VERSION_HEX >= 0x030400a1
+    0,
+#endif
+#if PY_VERSION_HEX >= 0x030800b1 && (!CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07030800)
+    0,
+#endif
+#if __PYX_NEED_TP_PRINT_SLOT
+    0,
+#endif
+#if PY_VERSION_HEX >= 0x030C0000
+    0,
+#endif
+#if PY_VERSION_HEX >= 0x030d00A4
+    0,
+#endif
+#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX >= 0x03090000 && PY_VERSION_HEX < 0x030a0000
+    0,
+#endif
+};
+#endif
+static int __pyx_CyFunction_init(PyObject *module) {
+#if CYTHON_USE_TYPE_SPECS
+    __pyx_CyFunctionType = __Pyx_FetchCommonTypeFromSpec(module, &__pyx_CyFunctionType_spec, NULL);
+#else
+    CYTHON_UNUSED_VAR(module);
+    __pyx_CyFunctionType = __Pyx_FetchCommonType(&__pyx_CyFunctionType_type);
+#endif
+    if (unlikely(__pyx_CyFunctionType == NULL)) {
+        return -1;
+    }
+    return 0;
+}
+static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *func, size_t size, int pyobjects) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->defaults = PyObject_Malloc(size);
+    if (unlikely(!m->defaults))
+        return PyErr_NoMemory();
+    memset(m->defaults, 0, size);
+    m->defaults_pyobjects = pyobjects;
+    m->defaults_size = size;
+    return m->defaults;
+}
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->defaults_tuple = tuple;
+    Py_INCREF(tuple);
+}
+static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->defaults_kwdict = dict;
+    Py_INCREF(dict);
+}
+static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) {
+    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
+    m->func_annotations = dict;
+    Py_INCREF(dict);
+}
+
+/* CythonFunction */
+  static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml, int flags, PyObject* qualname,
+                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
+    PyObject *op = __Pyx_CyFunction_Init(
+        PyObject_GC_New(__pyx_CyFunctionObject, __pyx_CyFunctionType),
+        ml, flags, qualname, closure, module, globals, code
+    );
+    if (likely(op)) {
+        PyObject_GC_Track(op);
+    }
+    return op;
+}
+
+/* PyDictVersioning */
+  #if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
+    PyObject *dict = Py_TYPE(obj)->tp_dict;
+    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
+}
+static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
+    PyObject **dictptr = NULL;
+    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
+    if (offset) {
+#if CYTHON_COMPILING_IN_CPYTHON
+        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
+#else
+        dictptr = _PyObject_GetDictPtr(obj);
+#endif
+    }
+    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
+}
+static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
+    PyObject *dict = Py_TYPE(obj)->tp_dict;
+    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
+        return 0;
+    return obj_dict_version == __Pyx_get_object_dict_version(obj);
+}
+#endif
+
+/* CLineInTraceback */
+  #ifndef CYTHON_CLINE_IN_TRACEBACK
+static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) {
+    PyObject *use_cline;
+    PyObject *ptype, *pvalue, *ptraceback;
+#if CYTHON_COMPILING_IN_CPYTHON
+    PyObject **cython_runtime_dict;
+#endif
+    CYTHON_MAYBE_UNUSED_VAR(tstate);
+    if (unlikely(!__pyx_cython_runtime)) {
+        return c_line;
+    }
+    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
+#if CYTHON_COMPILING_IN_CPYTHON
+    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
+    if (likely(cython_runtime_dict)) {
+        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
+            use_cline, *cython_runtime_dict,
+            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
+    } else
+#endif
+    {
+      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStrNoError(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
+      if (use_cline_obj) {
+        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
+        Py_DECREF(use_cline_obj);
+      } else {
+        PyErr_Clear();
+        use_cline = NULL;
+      }
+    }
+    if (!use_cline) {
+        c_line = 0;
+        (void) PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
+    }
+    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
+        c_line = 0;
+    }
+    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
+    return c_line;
+}
+#endif
+
+/* CodeObjectCache */
+  #if !CYTHON_COMPILING_IN_LIMITED_API
+static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
+    int start = 0, mid = 0, end = count - 1;
+    if (end >= 0 && code_line > entries[end].code_line) {
+        return count;
+    }
+    while (start < end) {
+        mid = start + (end - start) / 2;
+        if (code_line < entries[mid].code_line) {
+            end = mid;
+        } else if (code_line > entries[mid].code_line) {
+             start = mid + 1;
+        } else {
+            return mid;
+        }
+    }
+    if (code_line <= entries[mid].code_line) {
+        return mid;
+    } else {
+        return mid + 1;
+    }
+}
+static PyCodeObject *__pyx_find_code_object(int code_line) {
+    PyCodeObject* code_object;
+    int pos;
+    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
+        return NULL;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
+        return NULL;
+    }
+    code_object = __pyx_code_cache.entries[pos].code_object;
+    Py_INCREF(code_object);
+    return code_object;
+}
+static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
+    int pos, i;
+    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
+    if (unlikely(!code_line)) {
+        return;
+    }
+    if (unlikely(!entries)) {
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
+        if (likely(entries)) {
+            __pyx_code_cache.entries = entries;
+            __pyx_code_cache.max_count = 64;
+            __pyx_code_cache.count = 1;
+            entries[0].code_line = code_line;
+            entries[0].code_object = code_object;
+            Py_INCREF(code_object);
+        }
+        return;
+    }
+    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
+    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
+        PyCodeObject* tmp = entries[pos].code_object;
+        entries[pos].code_object = code_object;
+        Py_DECREF(tmp);
+        return;
+    }
+    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
+        int new_max = __pyx_code_cache.max_count + 64;
+        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
+            __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));
+        if (unlikely(!entries)) {
+            return;
+        }
+        __pyx_code_cache.entries = entries;
+        __pyx_code_cache.max_count = new_max;
+    }
+    for (i=__pyx_code_cache.count; i>pos; i--) {
+        entries[i] = entries[i-1];
+    }
+    entries[pos].code_line = code_line;
+    entries[pos].code_object = code_object;
+    __pyx_code_cache.count++;
+    Py_INCREF(code_object);
+}
+#endif
+
+/* AddTraceback */
+  #include "compile.h"
+#include "frameobject.h"
+#include "traceback.h"
+#if PY_VERSION_HEX >= 0x030b00a6 && !CYTHON_COMPILING_IN_LIMITED_API
+  #ifndef Py_BUILD_CORE
+    #define Py_BUILD_CORE 1
+  #endif
+  #include "internal/pycore_frame.h"
+#endif
+#if CYTHON_COMPILING_IN_LIMITED_API
+static PyObject *__Pyx_PyCode_Replace_For_AddTraceback(PyObject *code, PyObject *scratch_dict,
+                                                       PyObject *firstlineno, PyObject *name) {
+    PyObject *replace = NULL;
+    if (unlikely(PyDict_SetItemString(scratch_dict, "co_firstlineno", firstlineno))) return NULL;
+    if (unlikely(PyDict_SetItemString(scratch_dict, "co_name", name))) return NULL;
+    replace = PyObject_GetAttrString(code, "replace");
+    if (likely(replace)) {
+        PyObject *result;
+        result = PyObject_Call(replace, __pyx_empty_tuple, scratch_dict);
+        Py_DECREF(replace);
+        return result;
+    }
+    PyErr_Clear();
+    #if __PYX_LIMITED_VERSION_HEX < 0x030780000
+    {
+        PyObject *compiled = NULL, *result = NULL;
+        if (unlikely(PyDict_SetItemString(scratch_dict, "code", code))) return NULL;
+        if (unlikely(PyDict_SetItemString(scratch_dict, "type", (PyObject*)(&PyType_Type)))) return NULL;
+        compiled = Py_CompileString(
+            "out = type(code)(\n"
+            "  code.co_argcount, code.co_kwonlyargcount, code.co_nlocals, code.co_stacksize,\n"
+            "  code.co_flags, code.co_code, code.co_consts, code.co_names,\n"
+            "  code.co_varnames, code.co_filename, co_name, co_firstlineno,\n"
+            "  code.co_lnotab)\n", "<dummy>", Py_file_input);
+        if (!compiled) return NULL;
+        result = PyEval_EvalCode(compiled, scratch_dict, scratch_dict);
+        Py_DECREF(compiled);
+        if (!result) PyErr_Print();
+        Py_DECREF(result);
+        result = PyDict_GetItemString(scratch_dict, "out");
+        if (result) Py_INCREF(result);
+        return result;
+    }
+    #else
+    return NULL;
+    #endif
+}
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename) {
+    PyObject *code_object = NULL, *py_py_line = NULL, *py_funcname = NULL, *dict = NULL;
+    PyObject *replace = NULL, *getframe = NULL, *frame = NULL;
+    PyObject *exc_type, *exc_value, *exc_traceback;
+    int success = 0;
+    if (c_line) {
+        (void) __pyx_cfilenm;
+        (void) __Pyx_CLineForTraceback(__Pyx_PyThreadState_Current, c_line);
+    }
+    PyErr_Fetch(&exc_type, &exc_value, &exc_traceback);
+    code_object = Py_CompileString("_getframe()", filename, Py_eval_input);
+    if (unlikely(!code_object)) goto bad;
+    py_py_line = PyLong_FromLong(py_line);
+    if (unlikely(!py_py_line)) goto bad;
+    py_funcname = PyUnicode_FromString(funcname);
+    if (unlikely(!py_funcname)) goto bad;
+    dict = PyDict_New();
+    if (unlikely(!dict)) goto bad;
+    {
+        PyObject *old_code_object = code_object;
+        code_object = __Pyx_PyCode_Replace_For_AddTraceback(code_object, dict, py_py_line, py_funcname);
+        Py_DECREF(old_code_object);
+    }
+    if (unlikely(!code_object)) goto bad;
+    getframe = PySys_GetObject("_getframe");
+    if (unlikely(!getframe)) goto bad;
+    if (unlikely(PyDict_SetItemString(dict, "_getframe", getframe))) goto bad;
+    frame = PyEval_EvalCode(code_object, dict, dict);
+    if (unlikely(!frame) || frame == Py_None) goto bad;
+    success = 1;
+  bad:
+    PyErr_Restore(exc_type, exc_value, exc_traceback);
+    Py_XDECREF(code_object);
+    Py_XDECREF(py_py_line);
+    Py_XDECREF(py_funcname);
+    Py_XDECREF(dict);
+    Py_XDECREF(replace);
+    if (success) {
+        PyTraceBack_Here(
+            (struct _frame*)frame);
+    }
+    Py_XDECREF(frame);
+}
+#else
+static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
+            const char *funcname, int c_line,
+            int py_line, const char *filename) {
+    PyCodeObject *py_code = NULL;
+    PyObject *py_funcname = NULL;
+    #if PY_MAJOR_VERSION < 3
+    PyObject *py_srcfile = NULL;
+    py_srcfile = PyString_FromString(filename);
+    if (!py_srcfile) goto bad;
+    #endif
+    if (c_line) {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        if (!py_funcname) goto bad;
+        #else
+        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
+        if (!py_funcname) goto bad;
+        funcname = PyUnicode_AsUTF8(py_funcname);
+        if (!funcname) goto bad;
+        #endif
+    }
+    else {
+        #if PY_MAJOR_VERSION < 3
+        py_funcname = PyString_FromString(funcname);
+        if (!py_funcname) goto bad;
+        #endif
+    }
+    #if PY_MAJOR_VERSION < 3
+    py_code = __Pyx_PyCode_New(
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+        __pyx_empty_bytes, /*PyObject *code,*/
+        __pyx_empty_tuple, /*PyObject *consts,*/
+        __pyx_empty_tuple, /*PyObject *names,*/
+        __pyx_empty_tuple, /*PyObject *varnames,*/
+        __pyx_empty_tuple, /*PyObject *freevars,*/
+        __pyx_empty_tuple, /*PyObject *cellvars,*/
+        py_srcfile,   /*PyObject *filename,*/
+        py_funcname,  /*PyObject *name,*/
+        py_line,
+        __pyx_empty_bytes  /*PyObject *lnotab*/
+    );
+    Py_DECREF(py_srcfile);
+    #else
+    py_code = PyCode_NewEmpty(filename, funcname, py_line);
+    #endif
+    Py_XDECREF(py_funcname);
+    return py_code;
+bad:
+    Py_XDECREF(py_funcname);
+    #if PY_MAJOR_VERSION < 3
+    Py_XDECREF(py_srcfile);
+    #endif
+    return NULL;
+}
+static void __Pyx_AddTraceback(const char *funcname, int c_line,
+                               int py_line, const char *filename) {
+    PyCodeObject *py_code = 0;
+    PyFrameObject *py_frame = 0;
+    PyThreadState *tstate = __Pyx_PyThreadState_Current;
+    PyObject *ptype, *pvalue, *ptraceback;
+    if (c_line) {
+        c_line = __Pyx_CLineForTraceback(tstate, c_line);
+    }
+    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
+    if (!py_code) {
+        __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
+        py_code = __Pyx_CreateCodeObjectForTraceback(
+            funcname, c_line, py_line, filename);
+        if (!py_code) {
+            /* If the code object creation fails, then we should clear the
+               fetched exception references and propagate the new exception */
+            Py_XDECREF(ptype);
+            Py_XDECREF(pvalue);
+            Py_XDECREF(ptraceback);
+            goto bad;
+        }
+        __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
+        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
+    }
+    py_frame = PyFrame_New(
+        tstate,            /*PyThreadState *tstate,*/
+        py_code,           /*PyCodeObject *code,*/
+        __pyx_d,    /*PyObject *globals,*/
+        0                  /*PyObject *locals*/
+    );
+    if (!py_frame) goto bad;
+    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
+    PyTraceBack_Here(py_frame);
+bad:
+    Py_XDECREF(py_code);
+    Py_XDECREF(py_frame);
+}
+#endif
+
+#if PY_MAJOR_VERSION < 3
+static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
+    __Pyx_TypeName obj_type_name;
+    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
+    obj_type_name = __Pyx_PyType_GetName(Py_TYPE(obj));
+    PyErr_Format(PyExc_TypeError,
+                 "'" __Pyx_FMT_TYPENAME "' does not have the buffer interface",
+                 obj_type_name);
+    __Pyx_DECREF_TypeName(obj_type_name);
+    return -1;
+}
+static void __Pyx_ReleaseBuffer(Py_buffer *view) {
+    PyObject *obj = view->obj;
+    if (!obj) return;
+    if (PyObject_CheckBuffer(obj)) {
+        PyBuffer_Release(view);
+        return;
+    }
+    if ((0)) {}
+    view->obj = NULL;
+    Py_DECREF(obj);
+}
+#endif
+
+
+  /* CIntFromPyVerify */
+  #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
+#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
+    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
+#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
+    {\
+        func_type value = func_value;\
+        if (sizeof(target_type) < sizeof(func_type)) {\
+            if (unlikely(value != (func_type) (target_type) value)) {\
+                func_type zero = 0;\
+                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
+                    return (target_type) -1;\
+                if (is_unsigned && unlikely(value < zero))\
+                    goto raise_neg_overflow;\
+                else\
+                    goto raise_overflow;\
+            }\
+        }\
+        return (target_type) value;\
+    }
+
+/* Declarations */
+  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return ::std::complex< float >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      return x + y*(__pyx_t_float_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+      __pyx_t_float_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        __pyx_t_float_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabsf(b.real) >= fabsf(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                float r = b.imag / b.real;
+                float s = (float)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_float_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            float r = b.real / b.imag;
+            float s = (float)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_float_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            float denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_float_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
+        __pyx_t_float_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrtf(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypotf(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+            __pyx_t_float_complex z;
+            float r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    float denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_float(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_float(a, a);
+                        return __Pyx_c_prod_float(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_float(a, a);
+                        return __Pyx_c_prod_float(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if ((b.imag == 0) && (a.real >= 0)) {
+                    z.real = powf(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2f(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_float(a);
+                theta = atan2f(a.imag, a.real);
+            }
+            lnr = logf(r);
+            z_r = expf(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cosf(z_theta);
+            z.imag = z_r * sinf(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* Declarations */
+  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return ::std::complex< double >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      return x + y*(__pyx_t_double_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+      __pyx_t_double_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        __pyx_t_double_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabs(b.real) >= fabs(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                double r = b.imag / b.real;
+                double s = (double)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_double_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            double r = b.real / b.imag;
+            double s = (double)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_double_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            double denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_double_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
+        __pyx_t_double_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrt(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypot(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+            __pyx_t_double_complex z;
+            double r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    double denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_double(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_double(a, a);
+                        return __Pyx_c_prod_double(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_double(a, a);
+                        return __Pyx_c_prod_double(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if ((b.imag == 0) && (a.real >= 0)) {
+                    z.real = pow(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_double(a);
+                theta = atan2(a.imag, a.real);
+            }
+            lnr = log(r);
+            z_r = exp(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cos(z_theta);
+            z.imag = z_r * sin(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* Declarations */
+  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+  #ifdef __cplusplus
+    static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) {
+      return ::std::complex< long double >(x, y);
+    }
+  #else
+    static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) {
+      return x + y*(__pyx_t_long_double_complex)_Complex_I;
+    }
+  #endif
+#else
+    static CYTHON_INLINE __pyx_t_long_double_complex __pyx_t_long_double_complex_from_parts(long double x, long double y) {
+      __pyx_t_long_double_complex z;
+      z.real = x;
+      z.imag = y;
+      return z;
+    }
+#endif
+
+/* Arithmetic */
+  #if CYTHON_CCOMPLEX && (1) && (!0 || __cplusplus)
+#else
+    static CYTHON_INLINE int __Pyx_c_eq_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+       return (a.real == b.real) && (a.imag == b.imag);
+    }
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_sum_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+        __pyx_t_long_double_complex z;
+        z.real = a.real + b.real;
+        z.imag = a.imag + b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_diff_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+        __pyx_t_long_double_complex z;
+        z.real = a.real - b.real;
+        z.imag = a.imag - b.imag;
+        return z;
+    }
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_prod_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+        __pyx_t_long_double_complex z;
+        z.real = a.real * b.real - a.imag * b.imag;
+        z.imag = a.real * b.imag + a.imag * b.real;
+        return z;
+    }
+    #if 1
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else if (fabsl(b.real) >= fabsl(b.imag)) {
+            if (b.real == 0 && b.imag == 0) {
+                return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
+            } else {
+                long double r = b.imag / b.real;
+                long double s = (long double)(1.0) / (b.real + b.imag * r);
+                return __pyx_t_long_double_complex_from_parts(
+                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
+            }
+        } else {
+            long double r = b.real / b.imag;
+            long double s = (long double)(1.0) / (b.imag + b.real * r);
+            return __pyx_t_long_double_complex_from_parts(
+                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
+        }
+    }
+    #else
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_quot_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+        if (b.imag == 0) {
+            return __pyx_t_long_double_complex_from_parts(a.real / b.real, a.imag / b.real);
+        } else {
+            long double denom = b.real * b.real + b.imag * b.imag;
+            return __pyx_t_long_double_complex_from_parts(
+                (a.real * b.real + a.imag * b.imag) / denom,
+                (a.imag * b.real - a.real * b.imag) / denom);
+        }
+    }
+    #endif
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_neg_long__double(__pyx_t_long_double_complex a) {
+        __pyx_t_long_double_complex z;
+        z.real = -a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    static CYTHON_INLINE int __Pyx_c_is_zero_long__double(__pyx_t_long_double_complex a) {
+       return (a.real == 0) && (a.imag == 0);
+    }
+    static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_conj_long__double(__pyx_t_long_double_complex a) {
+        __pyx_t_long_double_complex z;
+        z.real =  a.real;
+        z.imag = -a.imag;
+        return z;
+    }
+    #if 1
+        static CYTHON_INLINE long double __Pyx_c_abs_long__double(__pyx_t_long_double_complex z) {
+          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
+            return sqrtl(z.real*z.real + z.imag*z.imag);
+          #else
+            return hypotl(z.real, z.imag);
+          #endif
+        }
+        static CYTHON_INLINE __pyx_t_long_double_complex __Pyx_c_pow_long__double(__pyx_t_long_double_complex a, __pyx_t_long_double_complex b) {
+            __pyx_t_long_double_complex z;
+            long double r, lnr, theta, z_r, z_theta;
+            if (b.imag == 0 && b.real == (int)b.real) {
+                if (b.real < 0) {
+                    long double denom = a.real * a.real + a.imag * a.imag;
+                    a.real = a.real / denom;
+                    a.imag = -a.imag / denom;
+                    b.real = -b.real;
+                }
+                switch ((int)b.real) {
+                    case 0:
+                        z.real = 1;
+                        z.imag = 0;
+                        return z;
+                    case 1:
+                        return a;
+                    case 2:
+                        return __Pyx_c_prod_long__double(a, a);
+                    case 3:
+                        z = __Pyx_c_prod_long__double(a, a);
+                        return __Pyx_c_prod_long__double(z, a);
+                    case 4:
+                        z = __Pyx_c_prod_long__double(a, a);
+                        return __Pyx_c_prod_long__double(z, z);
+                }
+            }
+            if (a.imag == 0) {
+                if (a.real == 0) {
+                    return a;
+                } else if ((b.imag == 0) && (a.real >= 0)) {
+                    z.real = powl(a.real, b.real);
+                    z.imag = 0;
+                    return z;
+                } else if (a.real > 0) {
+                    r = a.real;
+                    theta = 0;
+                } else {
+                    r = -a.real;
+                    theta = atan2l(0.0, -1.0);
+                }
+            } else {
+                r = __Pyx_c_abs_long__double(a);
+                theta = atan2l(a.imag, a.real);
+            }
+            lnr = logl(r);
+            z_r = expl(lnr * b.real - theta * b.imag);
+            z_theta = theta * b.real + lnr * b.imag;
+            z.real = z_r * cosl(z_theta);
+            z.imag = z_r * sinl(z_theta);
+            return z;
+        }
+    #endif
+#endif
+
+/* CIntFromPy */
+  static CYTHON_INLINE uint32_t __Pyx_PyInt_As_uint32_t(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const uint32_t neg_one = (uint32_t) -1, const_zero = (uint32_t) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if ((sizeof(uint32_t) < sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT(uint32_t, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (uint32_t) val;
+        }
+    }
+#endif
+    if (unlikely(!PyLong_Check(x))) {
+        uint32_t val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (uint32_t) -1;
+        val = __Pyx_PyInt_As_uint32_t(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+    if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
+            goto raise_neg_overflow;
+        } else if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(uint32_t, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_DigitCount(x)) {
+                case 2:
+                    if ((8 * sizeof(uint32_t) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) >= 2 * PyLong_SHIFT)) {
+                            return (uint32_t) (((((uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(uint32_t) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) >= 3 * PyLong_SHIFT)) {
+                            return (uint32_t) (((((((uint32_t)digits[2]) << PyLong_SHIFT) | (uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(uint32_t) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) >= 4 * PyLong_SHIFT)) {
+                            return (uint32_t) (((((((((uint32_t)digits[3]) << PyLong_SHIFT) | (uint32_t)digits[2]) << PyLong_SHIFT) | (uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0]));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
+        if (unlikely(Py_SIZE(x) < 0)) {
+            goto raise_neg_overflow;
+        }
+#else
+        {
+            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+            if (unlikely(result < 0))
+                return (uint32_t) -1;
+            if (unlikely(result == 1))
+                goto raise_neg_overflow;
+        }
+#endif
+        if ((sizeof(uint32_t) <= sizeof(unsigned long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint32_t, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(uint32_t) <= sizeof(unsigned PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint32_t, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+        }
+    } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(uint32_t, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_SignedDigitCount(x)) {
+                case -2:
+                    if ((8 * sizeof(uint32_t) - 1 > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) - 1 > 2 * PyLong_SHIFT)) {
+                            return (uint32_t) (((uint32_t)-1)*(((((uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if ((8 * sizeof(uint32_t) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) - 1 > 2 * PyLong_SHIFT)) {
+                            return (uint32_t) ((((((uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if ((8 * sizeof(uint32_t) - 1 > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) - 1 > 3 * PyLong_SHIFT)) {
+                            return (uint32_t) (((uint32_t)-1)*(((((((uint32_t)digits[2]) << PyLong_SHIFT) | (uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(uint32_t) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) - 1 > 3 * PyLong_SHIFT)) {
+                            return (uint32_t) ((((((((uint32_t)digits[2]) << PyLong_SHIFT) | (uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if ((8 * sizeof(uint32_t) - 1 > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) - 1 > 4 * PyLong_SHIFT)) {
+                            return (uint32_t) (((uint32_t)-1)*(((((((((uint32_t)digits[3]) << PyLong_SHIFT) | (uint32_t)digits[2]) << PyLong_SHIFT) | (uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(uint32_t) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint32_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint32_t) - 1 > 4 * PyLong_SHIFT)) {
+                            return (uint32_t) ((((((((((uint32_t)digits[3]) << PyLong_SHIFT) | (uint32_t)digits[2]) << PyLong_SHIFT) | (uint32_t)digits[1]) << PyLong_SHIFT) | (uint32_t)digits[0])));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+        if ((sizeof(uint32_t) <= sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint32_t, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(uint32_t) <= sizeof(PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint32_t, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+        }
+    }
+    {
+        uint32_t val;
+        int ret = -1;
+#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
+        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
+            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
+        if (unlikely(bytes_copied == -1)) {
+        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
+            goto raise_overflow;
+        } else {
+            ret = 0;
+        }
+#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
+        int one = 1; int is_little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&val;
+        ret = _PyLong_AsByteArray((PyLongObject *)x,
+                                    bytes, sizeof(val),
+                                    is_little, !is_unsigned);
+#else
+        PyObject *v;
+        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
+        int bits, remaining_bits, is_negative = 0;
+        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
+        if (likely(PyLong_CheckExact(x))) {
+            v = __Pyx_NewRef(x);
+        } else {
+            v = PyNumber_Long(x);
+            if (unlikely(!v)) return (uint32_t) -1;
+            assert(PyLong_CheckExact(v));
+        }
+        {
+            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
+            if (unlikely(result < 0)) {
+                Py_DECREF(v);
+                return (uint32_t) -1;
+            }
+            is_negative = result == 1;
+        }
+        if (is_unsigned && unlikely(is_negative)) {
+            Py_DECREF(v);
+            goto raise_neg_overflow;
+        } else if (is_negative) {
+            stepval = PyNumber_Invert(v);
+            Py_DECREF(v);
+            if (unlikely(!stepval))
+                return (uint32_t) -1;
+        } else {
+            stepval = v;
+        }
+        v = NULL;
+        val = (uint32_t) 0;
+        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
+        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
+        for (bits = 0; bits < (int) sizeof(uint32_t) * 8 - chunk_size; bits += chunk_size) {
+            PyObject *tmp, *digit;
+            long idigit;
+            digit = PyNumber_And(stepval, mask);
+            if (unlikely(!digit)) goto done;
+            idigit = PyLong_AsLong(digit);
+            Py_DECREF(digit);
+            if (unlikely(idigit < 0)) goto done;
+            val |= ((uint32_t) idigit) << bits;
+            tmp = PyNumber_Rshift(stepval, shift);
+            if (unlikely(!tmp)) goto done;
+            Py_DECREF(stepval); stepval = tmp;
+        }
+        Py_DECREF(shift); shift = NULL;
+        Py_DECREF(mask); mask = NULL;
+        {
+            long idigit = PyLong_AsLong(stepval);
+            if (unlikely(idigit < 0)) goto done;
+            remaining_bits = ((int) sizeof(uint32_t) * 8) - bits - (is_unsigned ? 0 : 1);
+            if (unlikely(idigit >= (1L << remaining_bits)))
+                goto raise_overflow;
+            val |= ((uint32_t) idigit) << bits;
+        }
+        if (!is_unsigned) {
+            if (unlikely(val & (((uint32_t) 1) << (sizeof(uint32_t) * 8 - 1))))
+                goto raise_overflow;
+            if (is_negative)
+                val = ~val;
+        }
+        ret = 0;
+    done:
+        Py_XDECREF(shift);
+        Py_XDECREF(mask);
+        Py_XDECREF(stepval);
+#endif
+        if (unlikely(ret))
+            return (uint32_t) -1;
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to uint32_t");
+    return (uint32_t) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to uint32_t");
+    return (uint32_t) -1;
+}
+
+/* CIntFromPy */
+  static CYTHON_INLINE uint16_t __Pyx_PyInt_As_uint16_t(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const uint16_t neg_one = (uint16_t) -1, const_zero = (uint16_t) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if ((sizeof(uint16_t) < sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT(uint16_t, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (uint16_t) val;
+        }
+    }
+#endif
+    if (unlikely(!PyLong_Check(x))) {
+        uint16_t val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (uint16_t) -1;
+        val = __Pyx_PyInt_As_uint16_t(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+    if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
+            goto raise_neg_overflow;
+        } else if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(uint16_t, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_DigitCount(x)) {
+                case 2:
+                    if ((8 * sizeof(uint16_t) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) >= 2 * PyLong_SHIFT)) {
+                            return (uint16_t) (((((uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(uint16_t) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) >= 3 * PyLong_SHIFT)) {
+                            return (uint16_t) (((((((uint16_t)digits[2]) << PyLong_SHIFT) | (uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(uint16_t) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) >= 4 * PyLong_SHIFT)) {
+                            return (uint16_t) (((((((((uint16_t)digits[3]) << PyLong_SHIFT) | (uint16_t)digits[2]) << PyLong_SHIFT) | (uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0]));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
+        if (unlikely(Py_SIZE(x) < 0)) {
+            goto raise_neg_overflow;
+        }
+#else
+        {
+            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+            if (unlikely(result < 0))
+                return (uint16_t) -1;
+            if (unlikely(result == 1))
+                goto raise_neg_overflow;
+        }
+#endif
+        if ((sizeof(uint16_t) <= sizeof(unsigned long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint16_t, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(uint16_t) <= sizeof(unsigned PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint16_t, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+        }
+    } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(uint16_t, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_SignedDigitCount(x)) {
+                case -2:
+                    if ((8 * sizeof(uint16_t) - 1 > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) - 1 > 2 * PyLong_SHIFT)) {
+                            return (uint16_t) (((uint16_t)-1)*(((((uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if ((8 * sizeof(uint16_t) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) - 1 > 2 * PyLong_SHIFT)) {
+                            return (uint16_t) ((((((uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if ((8 * sizeof(uint16_t) - 1 > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) - 1 > 3 * PyLong_SHIFT)) {
+                            return (uint16_t) (((uint16_t)-1)*(((((((uint16_t)digits[2]) << PyLong_SHIFT) | (uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(uint16_t) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) - 1 > 3 * PyLong_SHIFT)) {
+                            return (uint16_t) ((((((((uint16_t)digits[2]) << PyLong_SHIFT) | (uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if ((8 * sizeof(uint16_t) - 1 > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) - 1 > 4 * PyLong_SHIFT)) {
+                            return (uint16_t) (((uint16_t)-1)*(((((((((uint16_t)digits[3]) << PyLong_SHIFT) | (uint16_t)digits[2]) << PyLong_SHIFT) | (uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(uint16_t) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(uint16_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(uint16_t) - 1 > 4 * PyLong_SHIFT)) {
+                            return (uint16_t) ((((((((((uint16_t)digits[3]) << PyLong_SHIFT) | (uint16_t)digits[2]) << PyLong_SHIFT) | (uint16_t)digits[1]) << PyLong_SHIFT) | (uint16_t)digits[0])));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+        if ((sizeof(uint16_t) <= sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint16_t, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(uint16_t) <= sizeof(PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(uint16_t, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+        }
+    }
+    {
+        uint16_t val;
+        int ret = -1;
+#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
+        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
+            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
+        if (unlikely(bytes_copied == -1)) {
+        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
+            goto raise_overflow;
+        } else {
+            ret = 0;
+        }
+#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
+        int one = 1; int is_little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&val;
+        ret = _PyLong_AsByteArray((PyLongObject *)x,
+                                    bytes, sizeof(val),
+                                    is_little, !is_unsigned);
+#else
+        PyObject *v;
+        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
+        int bits, remaining_bits, is_negative = 0;
+        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
+        if (likely(PyLong_CheckExact(x))) {
+            v = __Pyx_NewRef(x);
+        } else {
+            v = PyNumber_Long(x);
+            if (unlikely(!v)) return (uint16_t) -1;
+            assert(PyLong_CheckExact(v));
+        }
+        {
+            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
+            if (unlikely(result < 0)) {
+                Py_DECREF(v);
+                return (uint16_t) -1;
+            }
+            is_negative = result == 1;
+        }
+        if (is_unsigned && unlikely(is_negative)) {
+            Py_DECREF(v);
+            goto raise_neg_overflow;
+        } else if (is_negative) {
+            stepval = PyNumber_Invert(v);
+            Py_DECREF(v);
+            if (unlikely(!stepval))
+                return (uint16_t) -1;
+        } else {
+            stepval = v;
+        }
+        v = NULL;
+        val = (uint16_t) 0;
+        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
+        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
+        for (bits = 0; bits < (int) sizeof(uint16_t) * 8 - chunk_size; bits += chunk_size) {
+            PyObject *tmp, *digit;
+            long idigit;
+            digit = PyNumber_And(stepval, mask);
+            if (unlikely(!digit)) goto done;
+            idigit = PyLong_AsLong(digit);
+            Py_DECREF(digit);
+            if (unlikely(idigit < 0)) goto done;
+            val |= ((uint16_t) idigit) << bits;
+            tmp = PyNumber_Rshift(stepval, shift);
+            if (unlikely(!tmp)) goto done;
+            Py_DECREF(stepval); stepval = tmp;
+        }
+        Py_DECREF(shift); shift = NULL;
+        Py_DECREF(mask); mask = NULL;
+        {
+            long idigit = PyLong_AsLong(stepval);
+            if (unlikely(idigit < 0)) goto done;
+            remaining_bits = ((int) sizeof(uint16_t) * 8) - bits - (is_unsigned ? 0 : 1);
+            if (unlikely(idigit >= (1L << remaining_bits)))
+                goto raise_overflow;
+            val |= ((uint16_t) idigit) << bits;
+        }
+        if (!is_unsigned) {
+            if (unlikely(val & (((uint16_t) 1) << (sizeof(uint16_t) * 8 - 1))))
+                goto raise_overflow;
+            if (is_negative)
+                val = ~val;
+        }
+        ret = 0;
+    done:
+        Py_XDECREF(shift);
+        Py_XDECREF(mask);
+        Py_XDECREF(stepval);
+#endif
+        if (unlikely(ret))
+            return (uint16_t) -1;
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to uint16_t");
+    return (uint16_t) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to uint16_t");
+    return (uint16_t) -1;
+}
+
+/* FormatTypeName */
+  #if CYTHON_COMPILING_IN_LIMITED_API
+static __Pyx_TypeName
+__Pyx_PyType_GetName(PyTypeObject* tp)
+{
+    PyObject *name = __Pyx_PyObject_GetAttrStr((PyObject *)tp,
+                                               __pyx_n_s_name);
+    if (unlikely(name == NULL) || unlikely(!PyUnicode_Check(name))) {
+        PyErr_Clear();
+        Py_XDECREF(name);
+        name = __Pyx_NewRef(__pyx_n_s__11);
+    }
+    return name;
+}
+#endif
+
+/* CIntToPy */
+  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const long neg_one = (long) -1, const_zero = (long) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+    if (is_unsigned) {
+        if (sizeof(long) < sizeof(long)) {
+            return PyInt_FromLong((long) value);
+        } else if (sizeof(long) <= sizeof(unsigned long)) {
+            return PyLong_FromUnsignedLong((unsigned long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
+            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
+#endif
+        }
+    } else {
+        if (sizeof(long) <= sizeof(long)) {
+            return PyInt_FromLong((long) value);
+#ifdef HAVE_LONG_LONG
+        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
+            return PyLong_FromLongLong((PY_LONG_LONG) value);
+#endif
+        }
+    }
+    {
+        unsigned char *bytes = (unsigned char *)&value;
+#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4
+        if (is_unsigned) {
+            return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1);
+        } else {
+            return PyLong_FromNativeBytes(bytes, sizeof(value), -1);
+        }
+#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        return _PyLong_FromByteArray(bytes, sizeof(long),
+                                     little, !is_unsigned);
+#else
+        int one = 1; int little = (int)*(unsigned char *)&one;
+        PyObject *from_bytes, *result = NULL;
+        PyObject *py_bytes = NULL, *arg_tuple = NULL, *kwds = NULL, *order_str = NULL;
+        from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes");
+        if (!from_bytes) return NULL;
+        py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(long));
+        if (!py_bytes) goto limited_bad;
+        order_str = PyUnicode_FromString(little ? "little" : "big");
+        if (!order_str) goto limited_bad;
+        arg_tuple = PyTuple_Pack(2, py_bytes, order_str);
+        if (!arg_tuple) goto limited_bad;
+        if (!is_unsigned) {
+            kwds = PyDict_New();
+            if (!kwds) goto limited_bad;
+            if (PyDict_SetItemString(kwds, "signed", __Pyx_NewRef(Py_True))) goto limited_bad;
+        }
+        result = PyObject_Call(from_bytes, arg_tuple, kwds);
+        limited_bad:
+        Py_XDECREF(kwds);
+        Py_XDECREF(arg_tuple);
+        Py_XDECREF(order_str);
+        Py_XDECREF(py_bytes);
+        Py_XDECREF(from_bytes);
+        return result;
+#endif
+    }
+}
+
+/* CIntFromPy */
+  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const long neg_one = (long) -1, const_zero = (long) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if ((sizeof(long) < sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (long) val;
+        }
+    }
+#endif
+    if (unlikely(!PyLong_Check(x))) {
+        long val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (long) -1;
+        val = __Pyx_PyInt_As_long(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+    if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
+            goto raise_neg_overflow;
+        } else if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_DigitCount(x)) {
+                case 2:
+                    if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) >= 2 * PyLong_SHIFT)) {
+                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) >= 3 * PyLong_SHIFT)) {
+                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) >= 4 * PyLong_SHIFT)) {
+                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
+        if (unlikely(Py_SIZE(x) < 0)) {
+            goto raise_neg_overflow;
+        }
+#else
+        {
+            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+            if (unlikely(result < 0))
+                return (long) -1;
+            if (unlikely(result == 1))
+                goto raise_neg_overflow;
+        }
+#endif
+        if ((sizeof(long) <= sizeof(unsigned long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(long) <= sizeof(unsigned PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+        }
+    } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_SignedDigitCount(x)) {
+                case -2:
+                    if ((8 * sizeof(long) - 1 > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
+                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
+                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
+                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
+                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) {
+                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) {
+                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+        if ((sizeof(long) <= sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(long) <= sizeof(PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+        }
+    }
+    {
+        long val;
+        int ret = -1;
+#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
+        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
+            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
+        if (unlikely(bytes_copied == -1)) {
+        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
+            goto raise_overflow;
+        } else {
+            ret = 0;
+        }
+#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
+        int one = 1; int is_little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&val;
+        ret = _PyLong_AsByteArray((PyLongObject *)x,
+                                    bytes, sizeof(val),
+                                    is_little, !is_unsigned);
+#else
+        PyObject *v;
+        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
+        int bits, remaining_bits, is_negative = 0;
+        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
+        if (likely(PyLong_CheckExact(x))) {
+            v = __Pyx_NewRef(x);
+        } else {
+            v = PyNumber_Long(x);
+            if (unlikely(!v)) return (long) -1;
+            assert(PyLong_CheckExact(v));
+        }
+        {
+            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
+            if (unlikely(result < 0)) {
+                Py_DECREF(v);
+                return (long) -1;
+            }
+            is_negative = result == 1;
+        }
+        if (is_unsigned && unlikely(is_negative)) {
+            Py_DECREF(v);
+            goto raise_neg_overflow;
+        } else if (is_negative) {
+            stepval = PyNumber_Invert(v);
+            Py_DECREF(v);
+            if (unlikely(!stepval))
+                return (long) -1;
+        } else {
+            stepval = v;
+        }
+        v = NULL;
+        val = (long) 0;
+        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
+        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
+        for (bits = 0; bits < (int) sizeof(long) * 8 - chunk_size; bits += chunk_size) {
+            PyObject *tmp, *digit;
+            long idigit;
+            digit = PyNumber_And(stepval, mask);
+            if (unlikely(!digit)) goto done;
+            idigit = PyLong_AsLong(digit);
+            Py_DECREF(digit);
+            if (unlikely(idigit < 0)) goto done;
+            val |= ((long) idigit) << bits;
+            tmp = PyNumber_Rshift(stepval, shift);
+            if (unlikely(!tmp)) goto done;
+            Py_DECREF(stepval); stepval = tmp;
+        }
+        Py_DECREF(shift); shift = NULL;
+        Py_DECREF(mask); mask = NULL;
+        {
+            long idigit = PyLong_AsLong(stepval);
+            if (unlikely(idigit < 0)) goto done;
+            remaining_bits = ((int) sizeof(long) * 8) - bits - (is_unsigned ? 0 : 1);
+            if (unlikely(idigit >= (1L << remaining_bits)))
+                goto raise_overflow;
+            val |= ((long) idigit) << bits;
+        }
+        if (!is_unsigned) {
+            if (unlikely(val & (((long) 1) << (sizeof(long) * 8 - 1))))
+                goto raise_overflow;
+            if (is_negative)
+                val = ~val;
+        }
+        ret = 0;
+    done:
+        Py_XDECREF(shift);
+        Py_XDECREF(mask);
+        Py_XDECREF(stepval);
+#endif
+        if (unlikely(ret))
+            return (long) -1;
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to long");
+    return (long) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to long");
+    return (long) -1;
+}
+
+/* CIntFromPy */
+  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wconversion"
+#endif
+    const int neg_one = (int) -1, const_zero = (int) 0;
+#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+    const int is_unsigned = neg_one > const_zero;
+#if PY_MAJOR_VERSION < 3
+    if (likely(PyInt_Check(x))) {
+        if ((sizeof(int) < sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
+        } else {
+            long val = PyInt_AS_LONG(x);
+            if (is_unsigned && unlikely(val < 0)) {
+                goto raise_neg_overflow;
+            }
+            return (int) val;
+        }
+    }
+#endif
+    if (unlikely(!PyLong_Check(x))) {
+        int val;
+        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
+        if (!tmp) return (int) -1;
+        val = __Pyx_PyInt_As_int(tmp);
+        Py_DECREF(tmp);
+        return val;
+    }
+    if (is_unsigned) {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
+            goto raise_neg_overflow;
+        } else if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_DigitCount(x)) {
+                case 2:
+                    if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) >= 2 * PyLong_SHIFT)) {
+                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) >= 3 * PyLong_SHIFT)) {
+                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) >= 4 * PyLong_SHIFT)) {
+                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
+        if (unlikely(Py_SIZE(x) < 0)) {
+            goto raise_neg_overflow;
+        }
+#else
+        {
+            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
+            if (unlikely(result < 0))
+                return (int) -1;
+            if (unlikely(result == 1))
+                goto raise_neg_overflow;
+        }
+#endif
+        if ((sizeof(int) <= sizeof(unsigned long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(int) <= sizeof(unsigned PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
+#endif
+        }
+    } else {
+#if CYTHON_USE_PYLONG_INTERNALS
+        if (__Pyx_PyLong_IsCompact(x)) {
+            __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
+        } else {
+            const digit* digits = __Pyx_PyLong_Digits(x);
+            assert(__Pyx_PyLong_DigitCount(x) > 1);
+            switch (__Pyx_PyLong_SignedDigitCount(x)) {
+                case -2:
+                    if ((8 * sizeof(int) - 1 > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
+                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 2:
+                    if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
+                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case -3:
+                    if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
+                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 3:
+                    if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
+                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case -4:
+                    if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) {
+                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+                case 4:
+                    if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) {
+                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
+                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
+                        } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) {
+                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
+                        }
+                    }
+                    break;
+            }
+        }
+#endif
+        if ((sizeof(int) <= sizeof(long))) {
+            __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
+#ifdef HAVE_LONG_LONG
+        } else if ((sizeof(int) <= sizeof(PY_LONG_LONG))) {
+            __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
+#endif
+        }
+    }
+    {
+        int val;
+        int ret = -1;
+#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
+        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
+            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
+        if (unlikely(bytes_copied == -1)) {
+        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
+            goto raise_overflow;
+        } else {
+            ret = 0;
+        }
+#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
+        int one = 1; int is_little = (int)*(unsigned char *)&one;
+        unsigned char *bytes = (unsigned char *)&val;
+        ret = _PyLong_AsByteArray((PyLongObject *)x,
+                                    bytes, sizeof(val),
+                                    is_little, !is_unsigned);
+#else
+        PyObject *v;
+        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
+        int bits, remaining_bits, is_negative = 0;
+        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
+        if (likely(PyLong_CheckExact(x))) {
+            v = __Pyx_NewRef(x);
+        } else {
+            v = PyNumber_Long(x);
+            if (unlikely(!v)) return (int) -1;
+            assert(PyLong_CheckExact(v));
+        }
+        {
+            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
+            if (unlikely(result < 0)) {
+                Py_DECREF(v);
+                return (int) -1;
+            }
+            is_negative = result == 1;
+        }
+        if (is_unsigned && unlikely(is_negative)) {
+            Py_DECREF(v);
+            goto raise_neg_overflow;
+        } else if (is_negative) {
+            stepval = PyNumber_Invert(v);
+            Py_DECREF(v);
+            if (unlikely(!stepval))
+                return (int) -1;
+        } else {
+            stepval = v;
+        }
+        v = NULL;
+        val = (int) 0;
+        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
+        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
+        for (bits = 0; bits < (int) sizeof(int) * 8 - chunk_size; bits += chunk_size) {
+            PyObject *tmp, *digit;
+            long idigit;
+            digit = PyNumber_And(stepval, mask);
+            if (unlikely(!digit)) goto done;
+            idigit = PyLong_AsLong(digit);
+            Py_DECREF(digit);
+            if (unlikely(idigit < 0)) goto done;
+            val |= ((int) idigit) << bits;
+            tmp = PyNumber_Rshift(stepval, shift);
+            if (unlikely(!tmp)) goto done;
+            Py_DECREF(stepval); stepval = tmp;
+        }
+        Py_DECREF(shift); shift = NULL;
+        Py_DECREF(mask); mask = NULL;
+        {
+            long idigit = PyLong_AsLong(stepval);
+            if (unlikely(idigit < 0)) goto done;
+            remaining_bits = ((int) sizeof(int) * 8) - bits - (is_unsigned ? 0 : 1);
+            if (unlikely(idigit >= (1L << remaining_bits)))
+                goto raise_overflow;
+            val |= ((int) idigit) << bits;
+        }
+        if (!is_unsigned) {
+            if (unlikely(val & (((int) 1) << (sizeof(int) * 8 - 1))))
+                goto raise_overflow;
+            if (is_negative)
+                val = ~val;
+        }
+        ret = 0;
+    done:
+        Py_XDECREF(shift);
+        Py_XDECREF(mask);
+        Py_XDECREF(stepval);
+#endif
+        if (unlikely(ret))
+            return (int) -1;
+        return val;
+    }
+raise_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "value too large to convert to int");
+    return (int) -1;
+raise_neg_overflow:
+    PyErr_SetString(PyExc_OverflowError,
+        "can't convert negative value to int");
+    return (int) -1;
+}
+
+/* FastTypeChecks */
+  #if CYTHON_COMPILING_IN_CPYTHON
+static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
+    while (a) {
+        a = __Pyx_PyType_GetSlot(a, tp_base, PyTypeObject*);
+        if (a == b)
+            return 1;
+    }
+    return b == &PyBaseObject_Type;
+}
+static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
+    PyObject *mro;
+    if (a == b) return 1;
+    mro = a->tp_mro;
+    if (likely(mro)) {
+        Py_ssize_t i, n;
+        n = PyTuple_GET_SIZE(mro);
+        for (i = 0; i < n; i++) {
+            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
+                return 1;
+        }
+        return 0;
+    }
+    return __Pyx_InBases(a, b);
+}
+static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b) {
+    PyObject *mro;
+    if (cls == a || cls == b) return 1;
+    mro = cls->tp_mro;
+    if (likely(mro)) {
+        Py_ssize_t i, n;
+        n = PyTuple_GET_SIZE(mro);
+        for (i = 0; i < n; i++) {
+            PyObject *base = PyTuple_GET_ITEM(mro, i);
+            if (base == (PyObject *)a || base == (PyObject *)b)
+                return 1;
+        }
+        return 0;
+    }
+    return __Pyx_InBases(cls, a) || __Pyx_InBases(cls, b);
+}
+#if PY_MAJOR_VERSION == 2
+static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
+    PyObject *exception, *value, *tb;
+    int res;
+    __Pyx_PyThreadState_declare
+    __Pyx_PyThreadState_assign
+    __Pyx_ErrFetch(&exception, &value, &tb);
+    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
+    if (unlikely(res == -1)) {
+        PyErr_WriteUnraisable(err);
+        res = 0;
+    }
+    if (!res) {
+        res = PyObject_IsSubclass(err, exc_type2);
+        if (unlikely(res == -1)) {
+            PyErr_WriteUnraisable(err);
+            res = 0;
+        }
+    }
+    __Pyx_ErrRestore(exception, value, tb);
+    return res;
+}
+#else
+static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
+    if (exc_type1) {
+        return __Pyx_IsAnySubtype2((PyTypeObject*)err, (PyTypeObject*)exc_type1, (PyTypeObject*)exc_type2);
+    } else {
+        return __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
+    }
+}
+#endif
+static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
+    Py_ssize_t i, n;
+    assert(PyExceptionClass_Check(exc_type));
+    n = PyTuple_GET_SIZE(tuple);
+#if PY_MAJOR_VERSION >= 3
+    for (i=0; i<n; i++) {
+        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
+    }
+#endif
+    for (i=0; i<n; i++) {
+        PyObject *t = PyTuple_GET_ITEM(tuple, i);
+        #if PY_MAJOR_VERSION < 3
+        if (likely(exc_type == t)) return 1;
+        #endif
+        if (likely(PyExceptionClass_Check(t))) {
+            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
+        } else {
+        }
+    }
+    return 0;
+}
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
+    if (likely(err == exc_type)) return 1;
+    if (likely(PyExceptionClass_Check(err))) {
+        if (likely(PyExceptionClass_Check(exc_type))) {
+            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
+        } else if (likely(PyTuple_Check(exc_type))) {
+            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
+        } else {
+        }
+    }
+    return PyErr_GivenExceptionMatches(err, exc_type);
+}
+static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
+    assert(PyExceptionClass_Check(exc_type1));
+    assert(PyExceptionClass_Check(exc_type2));
+    if (likely(err == exc_type1 || err == exc_type2)) return 1;
+    if (likely(PyExceptionClass_Check(err))) {
+        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
+    }
+    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
+}
+#endif
+
+/* CheckBinaryVersion */
+  static unsigned long __Pyx_get_runtime_version(void) {
+#if __PYX_LIMITED_VERSION_HEX >= 0x030B00A4
+    return Py_Version & ~0xFFUL;
+#else
+    const char* rt_version = Py_GetVersion();
+    unsigned long version = 0;
+    unsigned long factor = 0x01000000UL;
+    unsigned int digit = 0;
+    int i = 0;
+    while (factor) {
+        while ('0' <= rt_version[i] && rt_version[i] <= '9') {
+            digit = digit * 10 + (unsigned int) (rt_version[i] - '0');
+            ++i;
+        }
+        version += factor * digit;
+        if (rt_version[i] != '.')
+            break;
+        digit = 0;
+        factor >>= 8;
+        ++i;
+    }
+    return version;
+#endif
+}
+static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer) {
+    const unsigned long MAJOR_MINOR = 0xFFFF0000UL;
+    if ((rt_version & MAJOR_MINOR) == (ct_version & MAJOR_MINOR))
+        return 0;
+    if (likely(allow_newer && (rt_version & MAJOR_MINOR) > (ct_version & MAJOR_MINOR)))
+        return 1;
+    {
+        char message[200];
+        PyOS_snprintf(message, sizeof(message),
+                      "compile time Python version %d.%d "
+                      "of module '%.100s' "
+                      "%s "
+                      "runtime version %d.%d",
+                       (int) (ct_version >> 24), (int) ((ct_version >> 16) & 0xFF),
+                       __Pyx_MODULE_NAME,
+                       (allow_newer) ? "was newer than" : "does not match",
+                       (int) (rt_version >> 24), (int) ((rt_version >> 16) & 0xFF)
+       );
+        return PyErr_WarnEx(NULL, message, 1);
+    }
+}
+
+/* InitStrings */
+  #if PY_MAJOR_VERSION >= 3
+static int __Pyx_InitString(__Pyx_StringTabEntry t, PyObject **str) {
+    if (t.is_unicode | t.is_str) {
+        if (t.intern) {
+            *str = PyUnicode_InternFromString(t.s);
+        } else if (t.encoding) {
+            *str = PyUnicode_Decode(t.s, t.n - 1, t.encoding, NULL);
+        } else {
+            *str = PyUnicode_FromStringAndSize(t.s, t.n - 1);
+        }
+    } else {
+        *str = PyBytes_FromStringAndSize(t.s, t.n - 1);
+    }
+    if (!*str)
+        return -1;
+    if (PyObject_Hash(*str) == -1)
+        return -1;
+    return 0;
+}
+#endif
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
+    while (t->p) {
+        #if PY_MAJOR_VERSION >= 3
+        __Pyx_InitString(*t, t->p);
+        #else
+        if (t->is_unicode) {
+            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
+        } else if (t->intern) {
+            *t->p = PyString_InternFromString(t->s);
+        } else {
+            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
+        }
+        if (!*t->p)
+            return -1;
+        if (PyObject_Hash(*t->p) == -1)
+            return -1;
+        #endif
+        ++t;
+    }
+    return 0;
+}
+
+#include <string.h>
+static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s) {
+    size_t len = strlen(s);
+    if (unlikely(len > (size_t) PY_SSIZE_T_MAX)) {
+        PyErr_SetString(PyExc_OverflowError, "byte string is too long");
+        return -1;
+    }
+    return (Py_ssize_t) len;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
+    Py_ssize_t len = __Pyx_ssize_strlen(c_str);
+    if (unlikely(len < 0)) return NULL;
+    return __Pyx_PyUnicode_FromStringAndSize(c_str, len);
+}
+static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char* c_str) {
+    Py_ssize_t len = __Pyx_ssize_strlen(c_str);
+    if (unlikely(len < 0)) return NULL;
+    return PyByteArray_FromStringAndSize(c_str, len);
+}
+static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
+    Py_ssize_t ignore;
+    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
+}
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+#if !CYTHON_PEP393_ENABLED
+static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+    char* defenc_c;
+    PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
+    if (!defenc) return NULL;
+    defenc_c = PyBytes_AS_STRING(defenc);
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+    {
+        char* end = defenc_c + PyBytes_GET_SIZE(defenc);
+        char* c;
+        for (c = defenc_c; c < end; c++) {
+            if ((unsigned char) (*c) >= 128) {
+                PyUnicode_AsASCIIString(o);
+                return NULL;
+            }
+        }
+    }
+#endif
+    *length = PyBytes_GET_SIZE(defenc);
+    return defenc_c;
+}
+#else
+static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+    if (likely(PyUnicode_IS_ASCII(o))) {
+        *length = PyUnicode_GET_LENGTH(o);
+        return PyUnicode_AsUTF8(o);
+    } else {
+        PyUnicode_AsASCIIString(o);
+        return NULL;
+    }
+#else
+    return PyUnicode_AsUTF8AndSize(o, length);
+#endif
+}
+#endif
+#endif
+static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
+#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
+    if (
+#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
+            __Pyx_sys_getdefaultencoding_not_ascii &&
+#endif
+            PyUnicode_Check(o)) {
+        return __Pyx_PyUnicode_AsStringAndSize(o, length);
+    } else
+#endif
+#if (!CYTHON_COMPILING_IN_PYPY && !CYTHON_COMPILING_IN_LIMITED_API) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
+    if (PyByteArray_Check(o)) {
+        *length = PyByteArray_GET_SIZE(o);
+        return PyByteArray_AS_STRING(o);
+    } else
+#endif
+    {
+        char* result;
+        int r = PyBytes_AsStringAndSize(o, &result, length);
+        if (unlikely(r < 0)) {
+            return NULL;
+        } else {
+            return result;
+        }
+    }
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
+   int is_true = x == Py_True;
+   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
+   else return PyObject_IsTrue(x);
+}
+static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
+    int retval;
+    if (unlikely(!x)) return -1;
+    retval = __Pyx_PyObject_IsTrue(x);
+    Py_DECREF(x);
+    return retval;
+}
+static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
+    __Pyx_TypeName result_type_name = __Pyx_PyType_GetName(Py_TYPE(result));
+#if PY_MAJOR_VERSION >= 3
+    if (PyLong_Check(result)) {
+        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
+                "__int__ returned non-int (type " __Pyx_FMT_TYPENAME ").  "
+                "The ability to return an instance of a strict subclass of int is deprecated, "
+                "and may be removed in a future version of Python.",
+                result_type_name)) {
+            __Pyx_DECREF_TypeName(result_type_name);
+            Py_DECREF(result);
+            return NULL;
+        }
+        __Pyx_DECREF_TypeName(result_type_name);
+        return result;
+    }
+#endif
+    PyErr_Format(PyExc_TypeError,
+                 "__%.4s__ returned non-%.4s (type " __Pyx_FMT_TYPENAME ")",
+                 type_name, type_name, result_type_name);
+    __Pyx_DECREF_TypeName(result_type_name);
+    Py_DECREF(result);
+    return NULL;
+}
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
+#if CYTHON_USE_TYPE_SLOTS
+  PyNumberMethods *m;
+#endif
+  const char *name = NULL;
+  PyObject *res = NULL;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_Check(x) || PyLong_Check(x)))
+#else
+  if (likely(PyLong_Check(x)))
+#endif
+    return __Pyx_NewRef(x);
+#if CYTHON_USE_TYPE_SLOTS
+  m = Py_TYPE(x)->tp_as_number;
+  #if PY_MAJOR_VERSION < 3
+  if (m && m->nb_int) {
+    name = "int";
+    res = m->nb_int(x);
+  }
+  else if (m && m->nb_long) {
+    name = "long";
+    res = m->nb_long(x);
+  }
+  #else
+  if (likely(m && m->nb_int)) {
+    name = "int";
+    res = m->nb_int(x);
+  }
+  #endif
+#else
+  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
+    res = PyNumber_Int(x);
+  }
+#endif
+  if (likely(res)) {
+#if PY_MAJOR_VERSION < 3
+    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
+#else
+    if (unlikely(!PyLong_CheckExact(res))) {
+#endif
+        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
+    }
+  }
+  else if (!PyErr_Occurred()) {
+    PyErr_SetString(PyExc_TypeError,
+                    "an integer is required");
+  }
+  return res;
+}
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
+  Py_ssize_t ival;
+  PyObject *x;
+#if PY_MAJOR_VERSION < 3
+  if (likely(PyInt_CheckExact(b))) {
+    if (sizeof(Py_ssize_t) >= sizeof(long))
+        return PyInt_AS_LONG(b);
+    else
+        return PyInt_AsSsize_t(b);
+  }
+#endif
+  if (likely(PyLong_CheckExact(b))) {
+    #if CYTHON_USE_PYLONG_INTERNALS
+    if (likely(__Pyx_PyLong_IsCompact(b))) {
+        return __Pyx_PyLong_CompactValue(b);
+    } else {
+      const digit* digits = __Pyx_PyLong_Digits(b);
+      const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(b);
+      switch (size) {
+         case 2:
+           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -2:
+           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case 3:
+           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -3:
+           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case 4:
+           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
+             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+         case -4:
+           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
+             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
+           }
+           break;
+      }
+    }
+    #endif
+    return PyLong_AsSsize_t(b);
+  }
+  x = PyNumber_Index(b);
+  if (!x) return -1;
+  ival = PyInt_AsSsize_t(x);
+  Py_DECREF(x);
+  return ival;
+}
+static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject* o) {
+  if (sizeof(Py_hash_t) == sizeof(Py_ssize_t)) {
+    return (Py_hash_t) __Pyx_PyIndex_AsSsize_t(o);
+#if PY_MAJOR_VERSION < 3
+  } else if (likely(PyInt_CheckExact(o))) {
+    return PyInt_AS_LONG(o);
+#endif
+  } else {
+    Py_ssize_t ival;
+    PyObject *x;
+    x = PyNumber_Index(o);
+    if (!x) return -1;
+    ival = PyInt_AsLong(x);
+    Py_DECREF(x);
+    return ival;
+  }
+}
+static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
+  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
+}
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
+    return PyInt_FromSize_t(ival);
+}
+
+
+/* #### Code section: utility_code_pragmas_end ### */
+#ifdef _MSC_VER
+#pragma warning( pop )
+#endif
+
+
+
+/* #### Code section: end ### */
+#endif /* Py_PYTHON_H */
diff --git a/python_package/src/onlinemid/runningstats/runningstats.pyx b/python_package/src/onlinemid/runningstats/runningstats.pyx
index 46aa19d62e19227826710dfe79550444d19b76db..53b244b1b6318a7e8c8d2a8fc218fc395f1732c7 100644
--- a/python_package/src/onlinemid/runningstats/runningstats.pyx
+++ b/python_package/src/onlinemid/runningstats/runningstats.pyx
@@ -127,7 +127,7 @@ cpdef call_roi_stats(
         &data[0],
         image_size,
         num_images,
-        &online_roi[0],
+        &online_roi[0,0],
         num_rois,
         online_roi_length_per_roi,
         &litframes[0],
diff --git a/python_package/src/onlinemid/runningstats/runningstats_impl.cpp b/python_package/src/onlinemid/runningstats/runningstats_impl.cpp
index e944c0b80fea9f0fca09ccab07768c36a390d71f..ae9ba92bff7d3ff55df2e7d244991c36007845c1 100644
--- a/python_package/src/onlinemid/runningstats/runningstats_impl.cpp
+++ b/python_package/src/onlinemid/runningstats/runningstats_impl.cpp
@@ -580,7 +580,7 @@ void stats_with_roi(
         }
 
         // write result into memory
-        const auto res = local_roi_stats[this_roi].get();
+        const auto res = local_roi_stats.get();
         if (!res)
         {
             this_image_memory_mean[0] = 0.0;
@@ -638,7 +638,7 @@ void stats_with_roi(
             for (std::uint32_t litframe_idx = 0; litframe_idx < num_litframes; litframe_idx++ )
             {
                 const auto image_num = litframes[litframe_idx];
-                call_process_image_num(image_num);        
+                call_process_image_num(image_num, roi_num);        
             }
         }
     }
@@ -714,7 +714,7 @@ void stats_with_roi(
             const auto outputPtr = thisPixelOutputMem + 3*pixelNum;
             if (!res)
             {
-                outputPtr[0] = 0.0
+                outputPtr[0] = 0.0;
                 outputPtr[1] = INFINITY;
                 outputPtr[2] = INFINITY;
             }
diff --git a/python_package/src/onlinemid/runningstats/task_thread_pool.hpp b/python_package/src/onlinemid/runningstats/task_thread_pool.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..e8e282bf1dd6f2d88b4ea7a4bc48c1e841d2759b
--- /dev/null
+++ b/python_package/src/onlinemid/runningstats/task_thread_pool.hpp
@@ -0,0 +1,486 @@
+// SPDX-License-Identifier: BSD-2-Clause OR MIT OR BSL-1.0
+/**
+ * @brief A fast and lightweight thread pool for C++11 and newer.
+ * @see https://github.com/alugowski/task-thread-pool
+ * @author Adam Lugowski
+ * @copyright Copyright (C) 2023 Adam Lugowski.
+ *            Licensed under any of the following open-source licenses:
+ *            BSD-2-Clause license, MIT license, Boost Software License 1.0
+ *
+ *
+ * BSD-2-Clause license:
+ *
+ * Copyright (C) 2023 Adam Lugowski
+ * Redistribution and use in source and binary forms, with or without modification,
+ * are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice,
+ * this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ * this list of conditions and the following disclaimer in the documentation
+ * and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+ * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ *
+ *
+ * MIT License:
+ *
+ * Copyright (c) 2023 Adam Lugowski
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ *
+ *
+ * Boost Software License 1.0:
+ *
+ * Permission is hereby granted, free of charge, to any person or organization
+ * obtaining a copy of the software and accompanying documentation covered by
+ * this license (the "Software") to use, reproduce, display, distribute, execute,
+ * and transmit the Software, and to prepare derivative works of the Software,
+ * and to permit third-parties to whom the Software is furnished to do so,
+ * all subject to the following:
+ *
+ * The copyright notices in the Software and this entire statement, including
+ * the above license grant, this restriction and the following disclaimer, must
+ * be included in all copies of the Software, in whole or in part, and all
+ * derivative works of the Software, unless such copies or derivative works
+ * are solely in the form of machine-executable object code generated by a
+ * source language processor.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+ * SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+ * FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+#ifndef AL_TASK_THREAD_POOL_HPP
+#define AL_TASK_THREAD_POOL_HPP
+
+// Version macros.
+#define TASK_THREAD_POOL_VERSION_MAJOR 1
+#define TASK_THREAD_POOL_VERSION_MINOR 0
+#define TASK_THREAD_POOL_VERSION_PATCH 10
+
+#include <condition_variable>
+#include <functional>
+#include <future>
+#include <mutex>
+#include <queue>
+#include <thread>
+#include <type_traits>
+
+// MSVC does not correctly set the __cplusplus macro by default, so we must read it from _MSVC_LANG
+// See https://devblogs.microsoft.com/cppblog/msvc-now-correctly-reports-__cplusplus/
+#if __cplusplus >= 201703L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201703L)
+#define TTP_CXX17 1
+#else
+#define TTP_CXX17 0
+#endif
+
+#if TTP_CXX17
+#define TTP_NODISCARD [[nodiscard]]
+#else
+#define TTP_NODISCARD
+#endif
+
+namespace task_thread_pool {
+
+#if !TTP_CXX17
+    /**
+     * A reimplementation of std::decay_t, which is only available since C++14.
+     */
+    template <class T>
+    using decay_t = typename std::decay<T>::type;
+#endif
+
+    /**
+     * A fast and lightweight thread pool that uses C++11 threads.
+     */
+    class task_thread_pool {
+    public:
+        /**
+         * Create a task_thread_pool and start worker threads.
+         *
+         * @param num_threads Number of worker threads. If 0 then number of threads is equal to the
+         *                    number of physical cores on the machine, as given by std::thread::hardware_concurrency().
+         */
+        explicit task_thread_pool(unsigned int num_threads = 0) {
+            if (num_threads < 1) {
+                num_threads = std::thread::hardware_concurrency();
+                if (num_threads < 1) { num_threads = 1; }
+            }
+            start_threads(num_threads);
+        }
+
+        /**
+         * Finish all tasks left in the queue then shut down worker threads.
+         * If the pool is currently paused then it is resumed.
+         */
+        ~task_thread_pool() {
+            unpause();
+            wait_for_queued_tasks();
+            stop_all_threads();
+        }
+
+        /**
+         * Drop all tasks that have been submitted but not yet started by a worker.
+         *
+         * Tasks already in progress continue executing.
+         */
+        void clear_task_queue() {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            tasks = {};
+        }
+
+        /**
+         * Get number of enqueued tasks.
+         *
+         * @return Number of tasks that have been enqueued but not yet started.
+         */
+        TTP_NODISCARD size_t get_num_queued_tasks() const {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            return tasks.size();
+        }
+
+        /**
+         * Get number of in-progress tasks.
+         *
+         * @return Approximate number of tasks currently being processed by worker threads.
+         */
+        TTP_NODISCARD size_t get_num_running_tasks() const {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            return num_inflight_tasks;
+        }
+
+        /**
+         * Get total number of tasks in the pool.
+         *
+         * @return Approximate number of tasks both enqueued and running.
+         */
+        TTP_NODISCARD size_t get_num_tasks() const {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            return tasks.size() + num_inflight_tasks;
+        }
+
+        /**
+         * Get number of worker threads.
+         *
+         * @return Number of worker threads.
+         */
+        TTP_NODISCARD unsigned int get_num_threads() const {
+            const std::lock_guard<std::recursive_mutex> threads_lock(thread_mutex);
+            return static_cast<unsigned int>(threads.size());
+        }
+
+        /**
+         * Set number of worker threads. Will start or stop worker threads as necessary.
+         *
+         * @param num_threads Number of worker threads. If 0 then number of threads is equal to the
+         *                    number of physical cores on the machine, as given by std::thread::hardware_concurrency().
+         * @return Previous number of worker threads.
+         */
+        unsigned int set_num_threads(unsigned int num_threads) {
+            const std::lock_guard<std::recursive_mutex> threads_lock(thread_mutex);
+            unsigned int previous_num_threads = get_num_threads();
+
+            if (num_threads < 1) {
+                num_threads = std::thread::hardware_concurrency();
+                if (num_threads < 1) { num_threads = 1; }
+            }
+
+            if (previous_num_threads <= num_threads) {
+                // expanding the thread pool
+                start_threads(num_threads - previous_num_threads);
+            } else {
+                // contracting the thread pool
+                stop_all_threads();
+                {
+                    const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+                    pool_running = true;
+                }
+                start_threads(num_threads);
+            }
+
+            return previous_num_threads;
+        }
+
+        /**
+         * Stop executing queued tasks. Use `unpause()` to resume. Note: Destroying the pool will implicitly unpause.
+         *
+         * Any in-progress tasks continue executing.
+         */
+        void pause() {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            pool_paused = true;
+        }
+
+        /**
+         * Resume executing queued tasks.
+         */
+        void unpause() {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            pool_paused = false;
+            task_cv.notify_all();
+        }
+
+        /**
+         * Check whether the pool is paused.
+         *
+         * @return true if pause() has been called without an intervening unpause().
+         */
+        TTP_NODISCARD bool is_paused() const {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            return pool_paused;
+        }
+
+        /**
+         * Submit a Callable for the pool to execute and return a std::future.
+         *
+         * @param func The Callable to execute. Can be a function, a lambda, std::packaged_task, std::function, etc.
+         * @param args Arguments for func. Optional.
+         * @return std::future that can be used to get func's return value or thrown exception.
+         */
+        template <typename F, typename... A,
+#if TTP_CXX17
+            typename R = std::invoke_result_t<std::decay_t<F>, std::decay_t<A>...>
+#else
+            typename R = typename std::result_of<decay_t<F>(decay_t<A>...)>::type
+#endif
+            >
+        TTP_NODISCARD std::future<R> submit(F&& func, A&&... args) {
+#if defined(_MSC_VER)
+            // MSVC's packaged_task is not movable even though it should be.
+            // Discussion about this bug and its future fix:
+            // https://developercommunity.visualstudio.com/t/unable-to-move-stdpackaged-task-into-any-stl-conta/108672
+            std::shared_ptr<std::packaged_task<R()>> ptask =
+                std::make_shared<std::packaged_task<R()>>(std::bind(std::forward<F>(func), std::forward<A>(args)...));
+            submit_detach([ptask] { (*ptask)(); });
+            return ptask->get_future();
+#else
+            std::packaged_task<R()> task(std::bind(std::forward<F>(func), std::forward<A>(args)...));
+            auto ret = task.get_future();
+            submit_detach(std::move(task));
+            return ret;
+#endif
+        }
+
+        /**
+         * Submit a zero-argument Callable for the pool to execute.
+         *
+         * @param func The Callable to execute. Can be a function, a lambda, std::packaged_task, std::function, etc.
+         */
+        template <typename F>
+        void submit_detach(F&& func) {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            tasks.emplace(std::forward<F>(func));
+            task_cv.notify_one();
+        }
+
+        /**
+         * Submit a Callable with arguments for the pool to execute.
+         *
+         * @param func The Callable to execute. Can be a function, a lambda, std::packaged_task, std::function, etc.
+         */
+        template <typename F, typename... A>
+        void submit_detach(F&& func, A&&... args) {
+            const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+            tasks.emplace(std::bind(std::forward<F>(func), std::forward<A>(args)...));
+            task_cv.notify_one();
+        }
+
+        /**
+         * Block until the task queue is empty. Some tasks may be in-progress when this method returns.
+         */
+        void wait_for_queued_tasks() {
+            std::unique_lock<std::mutex> tasks_lock(task_mutex);
+            notify_task_finish = true;
+            task_finished_cv.wait(tasks_lock, [&] { return tasks.empty(); });
+            notify_task_finish = false;
+        }
+
+        /**
+         * Block until all tasks have finished.
+         */
+        void wait_for_tasks() {
+            std::unique_lock<std::mutex> tasks_lock(task_mutex);
+            notify_task_finish = true;
+            task_finished_cv.wait(tasks_lock, [&] { return tasks.empty() && num_inflight_tasks == 0; });
+            notify_task_finish = false;
+        }
+
+    protected:
+
+        /**
+         * Main function for worker threads.
+         */
+        void worker_main() {
+            bool finished_task = false;
+
+            while (true) {
+                std::unique_lock<std::mutex> tasks_lock(task_mutex);
+
+                if (finished_task) {
+                    --num_inflight_tasks;
+                    if (notify_task_finish) {
+                        task_finished_cv.notify_all();
+                    }
+                }
+
+                task_cv.wait(tasks_lock, [&]() { return !pool_running || (!pool_paused && !tasks.empty()); });
+
+                if (!pool_running) {
+                    break;
+                }
+
+                // Must mean that (!pool_paused && !tasks.empty()) is true
+
+                std::packaged_task<void()> task{std::move(tasks.front())};
+                tasks.pop();
+                ++num_inflight_tasks;
+                tasks_lock.unlock();
+
+                try {
+                    task();
+                } catch (...) {
+                    // std::packaged_task::operator() may throw in some error conditions, such as if the task
+                    // had already been run. Nothing that the pool can do anything about.
+                }
+
+                finished_task = true;
+            }
+        }
+
+        /**
+         * Start worker threads.
+         *
+         * @param num_threads How many threads to start.
+         */
+        void start_threads(const unsigned int num_threads) {
+            const std::lock_guard<std::recursive_mutex> threads_lock(thread_mutex);
+
+            for (unsigned int i = 0; i < num_threads; ++i) {
+                threads.emplace_back(&task_thread_pool::worker_main, this);
+            }
+        }
+
+        /**
+         * Stop, join, and destroy all worker threads.
+         */
+        void stop_all_threads() {
+            const std::lock_guard<std::recursive_mutex> threads_lock(thread_mutex);
+
+            {
+                const std::lock_guard<std::mutex> tasks_lock(task_mutex);
+                pool_running = false;
+                task_cv.notify_all();
+            }
+
+            for (auto& thread : threads) {
+                if (thread.joinable()) {
+                    thread.join();
+                }
+            }
+            threads.clear();
+        }
+
+        /**
+         * The worker threads.
+         *
+         * Access protected by thread_mutex
+         */
+        std::vector<std::thread> threads;
+
+        /**
+         * A mutex for methods that start/stop threads.
+         */
+        mutable std::recursive_mutex thread_mutex;
+
+        /**
+         * The task queue.
+         *
+         * Access protected by task_mutex.
+         */
+        std::queue<std::packaged_task<void()>> tasks = {};
+
+        /**
+         * A mutex for all variables related to tasks.
+         */
+        mutable std::mutex task_mutex;
+
+        /**
+         * Used to notify changes to the task queue, such as a new task added, pause/unpause, etc.
+         */
+        std::condition_variable task_cv;
+
+        /**
+         * Used to notify of finished tasks.
+         */
+        std::condition_variable task_finished_cv;
+
+        /**
+         * A signal for worker threads that the pool is either running or shutting down.
+         *
+         * Access protected by task_mutex.
+         */
+        bool pool_running = true;
+
+        /**
+         * A signal for worker threads to not pull new tasks from the queue.
+         *
+         * Access protected by task_mutex.
+         */
+        bool pool_paused = false;
+
+        /**
+         * A signal for worker threads that they should notify task_finished_cv when they finish a task.
+         *
+         * Access protected by task_mutex.
+         */
+        bool notify_task_finish = false;
+
+        /**
+         * A counter of the number of tasks in-progress by worker threads.
+         * Incremented when a task is popped off the task queue and decremented when that task is complete.
+         *
+         * Access protected by task_mutex.
+         */
+        int num_inflight_tasks = 0;
+    };
+}
+
+// clean up
+#undef TTP_NODISCARD
+#undef TTP_CXX17
+
+#endif
\ No newline at end of file