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/* BEGIN: Cython Metadata
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END: Cython Metadata */

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#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
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#if PY_MAJOR_VERSION >= 3
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#define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
#define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
#elif CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
typedef struct {
    unaryfunc am_await;
    unaryfunc am_aiter;
    unaryfunc am_anext;
} __Pyx_PyAsyncMethodsStruct;
#define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
#else
#define __Pyx_PyType_AsAsync(obj) NULL
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#ifndef CYTHON_RESTRICT
  #if defined(__GNUC__)
    #define CYTHON_RESTRICT __restrict__
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    #define CYTHON_RESTRICT __restrict
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_RESTRICT restrict
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    #define CYTHON_RESTRICT
  #endif
#endif
#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)

#ifndef __cplusplus
  #error "Cython files generated with the C++ option must be compiled with a C++ compiler."
#endif
#ifndef CYTHON_INLINE
  #define CYTHON_INLINE inline
#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; }
    operator T&() { return *ptr; }
  private:
    T *ptr;
};

#if defined(WIN32) || defined(MS_WINDOWS)
  #define _USE_MATH_DEFINES
#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 PY_MAJOR_VERSION >= 3
  #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

#ifndef __PYX_EXTERN_C
  #ifdef __cplusplus
    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif

#define __PYX_HAVE__knorPy__knor__knor
#define __PYX_HAVE_API__knorPy__knor__knor
#include <vector>
#include "ios"
#include "new"
#include "stdexcept"
#include "typeinfo"
#include "string.h"
#include <string>
#include "stdint.h"
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "kmeans_types.hpp"
#include "util.hpp"
#include "knori.hpp"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#ifdef PYREX_WITHOUT_ASSERTIONS
#define CYTHON_WITHOUT_ASSERTIONS
#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_NCP_UNUSED
# if CYTHON_COMPILING_IN_CPYTHON
#  define CYTHON_NCP_UNUSED
# else
#  define CYTHON_NCP_UNUSED CYTHON_UNUSED
# endif
#endif
typedef struct {PyObject **p; 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_DEFAULT 0
#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)))  )
#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) && defined (_M_X64)
    #define __Pyx_sst_abs(value) _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 char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
#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_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((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)
#if PY_MAJOR_VERSION < 3
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
{
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#else
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
#endif
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x);
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_COMPILING_IN_CPYTHON
#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 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
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] = 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
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));
    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 PyObject *__pyx_m;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

#if !defined(CYTHON_CCOMPLEX)
  #if defined(__cplusplus)
    #define CYTHON_CCOMPLEX 1
  #elif defined(_Complex_I)
    #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


static const char *__pyx_f[] = {
  "knorPy/knor/knor.pyx",
  "__init__.pxd",
  "knorPy/stringsource",
  "type.pxd",
};

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":725
 * # 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;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":726
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 * ctypedef npy_int64      int64_t
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typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":727
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":728
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":732
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":733
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 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":734
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 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":735
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":739
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":740
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":749
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":750
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":751
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":753
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":754
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":755
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":757
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":758
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":760
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":761
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/* "../../../../usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":764
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/* Module declarations from 'libc.string' */

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static std::vector<size_t>  __pyx_convert_vector_from_py_size_t(PyObject *); /*proto*/
static std::vector<double>  __pyx_convert_vector_from_py_double(PyObject *); /*proto*/
static std::string __pyx_convert_string_from_py_std__in_string(PyObject *); /*proto*/
static PyObject *__pyx_convert_vector_to_py_unsigned_int(const std::vector<unsigned int>  &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_size_t(const std::vector<size_t>  &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_double(const std::vector<double>  &); /*proto*/
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static char __pyx_k_b[] = "b";
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static char __pyx_k_g[] = "g";
static char __pyx_k_h[] = "h";
static char __pyx_k_i[] = "i";
static char __pyx_k_k[] = "k";
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static char __pyx_k_np[] = "np";
static char __pyx_k_os[] = "os";
static char __pyx_k_omp[] = "omp";
static char __pyx_k_ret[] = "ret";
static char __pyx_k_sys[] = "sys";
static char __pyx_k_addr[] = "addr";
static char __pyx_k_data[] = "data";
static char __pyx_k_eucl[] = "eucl";
static char __pyx_k_init[] = "init";
static char __pyx_k_item[] = "item";
static char __pyx_k_join[] = "join";
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static char __pyx_k_main[] = "__main__";
static char __pyx_k_ncol[] = "ncol";
static char __pyx_k_ndim[] = "ndim";
static char __pyx_k_none[] = "none";
static char __pyx_k_nrow[] = "nrow";
static char __pyx_k_test[] = "__test__";
static char __pyx_k_utf8[] = "utf8";
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static char __pyx_k_iters[] = "iters";
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static char __pyx_k_kmeanspp[] = "kmeanspp";
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static char __pyx_k_transpose[] = "transpose";
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static char __pyx_k_maintainer[] = "__maintainer__";
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static char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
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static char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
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static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
static PyObject *__pyx_kp_s_Iterations_k_Sizes_Centroids_Clu;
static PyObject *__pyx_n_s_Kmeans;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_NotImplementedError;
static PyObject *__pyx_n_s_PYTHON_VERSION;
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static PyObject *__pyx_n_s_Pyx_CFunc_unsigned__int;
static PyObject *__pyx_n_s_RuntimeError;
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static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s_abspath;
static PyObject *__pyx_n_s_addr;
static PyObject *__pyx_n_s_array;
static PyObject *__pyx_n_s_array_equal;
static PyObject *__pyx_n_s_assignment_count_buf;
static PyObject *__pyx_n_s_assignments_buf;
static PyObject *__pyx_n_s_author;
static PyObject *__pyx_n_s_build_defaults;
static PyObject *__pyx_n_s_c_centers;
static PyObject *__pyx_n_s_c_void_p;
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static PyObject *__pyx_n_s_centroids;
static PyObject *__pyx_n_s_cfunc_to_py;
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static PyObject *__pyx_n_s_isfortran;
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static PyObject *__pyx_n_s_join;
static PyObject *__pyx_n_s_k;
static PyObject *__pyx_n_s_kmeanspp;
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static PyObject *__pyx_n_s_knorPy_knor_knor;
static PyObject *__pyx_n_s_kwargs;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_maintainer;
static PyObject *__pyx_n_s_max_iters;
static PyObject *__pyx_n_s_maxsize;
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    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_New(1);
    if (unlikely(!args)) return NULL;
    Py_INCREF(arg);
    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
            return __Pyx_PyObject_CallMethO(func, arg);
        }
    }
    return __Pyx__PyObject_CallOneArg(func, arg);
}
#else
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_Pack(1, arg);
    if (unlikely(!args)) return NULL;
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
            return __Pyx_PyObject_CallMethO(func, NULL);
        }
    }
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
}
#endif

static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
    if (unlikely(!result)) {
        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;
}

static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if CYTHON_COMPILING_IN_CPYTHON
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

static CYTHON_INLINE int __Pyx_IterFinish(void) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    PyObject* exc_type = tstate->curexc_type;
    if (unlikely(exc_type)) {
        if (likely(exc_type == PyExc_StopIteration) || PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration)) {
            PyObject *exc_value, *exc_tb;
            exc_value = tstate->curexc_value;
            exc_tb = tstate->curexc_traceback;
            tstate->curexc_type = 0;
            tstate->curexc_value = 0;
            tstate->curexc_traceback = 0;
            Py_DECREF(exc_type);
            Py_XDECREF(exc_value);
            Py_XDECREF(exc_tb);
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#else
    if (unlikely(PyErr_Occurred())) {
        if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
            PyErr_Clear();
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#endif
}

static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name) {
    PyObject *method, *result = NULL;
    method = __Pyx_PyObject_GetAttrStr(obj, method_name);
    if (unlikely(!method)) goto bad;
#if CYTHON_COMPILING_IN_CPYTHON
    if (likely(PyMethod_Check(method))) {
        PyObject *self = PyMethod_GET_SELF(method);
        if (likely(self)) {
            PyObject *function = PyMethod_GET_FUNCTION(method);
            result = __Pyx_PyObject_CallOneArg(function, self);
            Py_DECREF(method);
            return result;
        }
    }
#endif
    result = __Pyx_PyObject_CallNoArg(method);
    Py_DECREF(method);
bad:
    return result;
}

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
    if (unlikely(retval)) {
        Py_DECREF(retval);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    } else {
        return __Pyx_IterFinish();
    }
    return 0;
}

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

static void __Pyx_UnpackTupleError(PyObject *t, Py_ssize_t index) {
    if (t == Py_None) {
      __Pyx_RaiseNoneNotIterableError();
    } else if (PyTuple_GET_SIZE(t) < index) {
      __Pyx_RaiseNeedMoreValuesError(PyTuple_GET_SIZE(t));
    } else {
      __Pyx_RaiseTooManyValuesError(index);
    }
}

static CYTHON_INLINE int __Pyx_unpack_tuple2(PyObject* tuple, PyObject** pvalue1, PyObject** pvalue2,
                                             int is_tuple, int has_known_size, int decref_tuple) {
    Py_ssize_t index;
    PyObject *value1 = NULL, *value2 = NULL, *iter = NULL;
    if (!is_tuple && unlikely(!PyTuple_Check(tuple))) {
        iternextfunc iternext;
        iter = PyObject_GetIter(tuple);
        if (unlikely(!iter)) goto bad;
        if (decref_tuple) { Py_DECREF(tuple); tuple = NULL; }
        iternext = Py_TYPE(iter)->tp_iternext;
        value1 = iternext(iter); if (unlikely(!value1)) { index = 0; goto unpacking_failed; }
        value2 = iternext(iter); if (unlikely(!value2)) { index = 1; goto unpacking_failed; }
        if (!has_known_size && unlikely(__Pyx_IternextUnpackEndCheck(iternext(iter), 2))) goto bad;
        Py_DECREF(iter);
    } else {
        if (!has_known_size && unlikely(PyTuple_GET_SIZE(tuple) != 2)) {
            __Pyx_UnpackTupleError(tuple, 2);
            goto bad;
        }
#if CYTHON_COMPILING_IN_PYPY
        value1 = PySequence_ITEM(tuple, 0);
        if (unlikely(!value1)) goto bad;
        value2 = PySequence_ITEM(tuple, 1);
        if (unlikely(!value2)) goto bad;
#else
        value1 = PyTuple_GET_ITEM(tuple, 0);
        value2 = PyTuple_GET_ITEM(tuple, 1);
        Py_INCREF(value1);
        Py_INCREF(value2);
#endif
        if (decref_tuple) { Py_DECREF(tuple); }
    }
    *pvalue1 = value1;
    *pvalue2 = value2;
    return 0;
unpacking_failed:
    if (!has_known_size && __Pyx_IterFinish() == 0)
        __Pyx_RaiseNeedMoreValuesError(index);
bad:
    Py_XDECREF(iter);
    Py_XDECREF(value1);
    Py_XDECREF(value2);
    if (decref_tuple) { Py_XDECREF(tuple); }
    return -1;
}

static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* iterable, int is_dict, PyObject* method_name,
                                                   Py_ssize_t* p_orig_length, int* p_source_is_dict) {
    is_dict = is_dict || likely(PyDict_CheckExact(iterable));
    *p_source_is_dict = is_dict;
#if !CYTHON_COMPILING_IN_PYPY
    if (is_dict) {
        *p_orig_length = PyDict_Size(iterable);
        Py_INCREF(iterable);
        return iterable;
    }
#endif
    *p_orig_length = 0;
    if (method_name) {
        PyObject* iter;
        iterable = __Pyx_PyObject_CallMethod0(iterable, method_name);
        if (!iterable)
            return NULL;
#if !CYTHON_COMPILING_IN_PYPY
        if (PyTuple_CheckExact(iterable) || PyList_CheckExact(iterable))
            return iterable;
#endif
        iter = PyObject_GetIter(iterable);
        Py_DECREF(iterable);
        return iter;
    }
    return PyObject_GetIter(iterable);
}
static CYTHON_INLINE int __Pyx_dict_iter_next(
        PyObject* iter_obj, CYTHON_NCP_UNUSED Py_ssize_t orig_length, CYTHON_NCP_UNUSED Py_ssize_t* ppos,
        PyObject** pkey, PyObject** pvalue, PyObject** pitem, int source_is_dict) {
    PyObject* next_item;
#if !CYTHON_COMPILING_IN_PYPY
    if (source_is_dict) {
        PyObject *key, *value;
        if (unlikely(orig_length != PyDict_Size(iter_obj))) {
            PyErr_SetString(PyExc_RuntimeError, "dictionary changed size during iteration");
            return -1;
        }
        if (unlikely(!PyDict_Next(iter_obj, ppos, &key, &value))) {
            return 0;
        }
        if (pitem) {
            PyObject* tuple = PyTuple_New(2);
            if (unlikely(!tuple)) {
                return -1;
            }
            Py_INCREF(key);
            Py_INCREF(value);
            PyTuple_SET_ITEM(tuple, 0, key);
            PyTuple_SET_ITEM(tuple, 1, value);
            *pitem = tuple;
        } else {
            if (pkey) {
                Py_INCREF(key);
                *pkey = key;
            }
            if (pvalue) {
                Py_INCREF(value);
                *pvalue = value;
            }
        }
        return 1;
    } else if (PyTuple_CheckExact(iter_obj)) {
        Py_ssize_t pos = *ppos;
        if (unlikely(pos >= PyTuple_GET_SIZE(iter_obj))) return 0;
        *ppos = pos + 1;
        next_item = PyTuple_GET_ITEM(iter_obj, pos);
        Py_INCREF(next_item);
    } else if (PyList_CheckExact(iter_obj)) {
        Py_ssize_t pos = *ppos;
        if (unlikely(pos >= PyList_GET_SIZE(iter_obj))) return 0;
        *ppos = pos + 1;
        next_item = PyList_GET_ITEM(iter_obj, pos);
        Py_INCREF(next_item);
    } else
#endif
    {
        next_item = PyIter_Next(iter_obj);
        if (unlikely(!next_item)) {
            return __Pyx_IterFinish();
        }
    }
    if (pitem) {
        *pitem = next_item;
    } else if (pkey && pvalue) {
        if (__Pyx_unpack_tuple2(next_item, pkey, pvalue, source_is_dict, source_is_dict, 1))
            return -1;
    } else if (pkey) {
        *pkey = next_item;
    } else {
        *pvalue = next_item;
    }
    return 1;
}

#if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_EqObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    if (op1 == op2) {
        Py_RETURN_TRUE;
    }
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long a = PyInt_AS_LONG(op1);
        if (a == b) {
            Py_RETURN_TRUE;
        } else {
            Py_RETURN_FALSE;
        }
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a;
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    }
                #if PyLong_SHIFT < 30 && PyLong_SHIFT != 15
                default: return PyLong_Type.tp_richcompare(op1, op2, Py_EQ);
                #else
                default: Py_RETURN_FALSE;
                #endif
            }
        }
            if (a == b) {
                Py_RETURN_TRUE;
            } else {
                Py_RETURN_FALSE;
            }
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            if ((double)a == (double)b) {
                Py_RETURN_TRUE;
            } else {
                Py_RETURN_FALSE;
            }
    }
    return PyObject_RichCompare(op1, op2, Py_EQ);
}
#endif

static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    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);
#else
    PyErr_Restore(type, value, tb);
#endif
}
static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(type, value, tb);
#endif
}

#if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *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_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 PY_VERSION_HEX >= 0x03030000
    if (cause) {
#else
    if (cause && cause != Py_None) {
#endif
        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 CYTHON_COMPILING_IN_PYPY
        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);
#else
        PyThreadState *tstate = PyThreadState_GET();
        PyObject* tmp_tb = tstate->curexc_traceback;
        if (tb != tmp_tb) {
            Py_INCREF(tb);
            tstate->curexc_traceback = tb;
            Py_XDECREF(tmp_tb);
        }
#endif
    }
bad:
    Py_XDECREF(owned_instance);
    return;
}
#endif

static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (!j) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyList_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
                                                     CYTHON_NCP_UNUSED int wraparound,
                                                     CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
            PyObject *r = PyList_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (PyErr_ExceptionMatches(PyExc_OverflowError))
                        PyErr_Clear();
                    else
                        return NULL;
                }
            }
            return m->sq_item(o, i);
        }
    }
#else
    if (is_list || PySequence_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
}

static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (likely(PyObject_TypeCheck(obj, type)))
        return 1;
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                 Py_TYPE(obj)->tp_name, type->tp_name);
    return 0;
}

static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
    PyObject* fake_module;
    PyTypeObject* cached_type = NULL;
    fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
    if (!fake_module) return NULL;
    Py_INCREF(fake_module);
    cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
    if (cached_type) {
        if (!PyType_Check((PyObject*)cached_type)) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s is not a type object",
                type->tp_name);
            goto bad;
        }
        if (cached_type->tp_basicsize != type->tp_basicsize) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s has the wrong size, try recompiling",
                type->tp_name);
            goto bad;
        }
    } else {
        if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
        PyErr_Clear();
        if (PyType_Ready(type) < 0) goto bad;
        if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
            goto bad;
        Py_INCREF(type);
        cached_type = type;
    }
done:
    Py_DECREF(fake_module);
    return cached_type;
bad:
    Py_XDECREF(cached_type);
    cached_type = NULL;
    goto done;
}

static PyObject *
__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *closure)
{
    if (unlikely(op->func_doc == NULL)) {
        if (op->func.m_ml->ml_doc) {
#if PY_MAJOR_VERSION >= 3
            op->func_doc = PyUnicode_FromString(op->func.m_ml->ml_doc);
#else
            op->func_doc = PyString_FromString(op->func.m_ml->ml_doc);
#endif
            if (unlikely(op->func_doc == NULL))
                return NULL;
        } else {
            Py_INCREF(Py_None);
            return Py_None;
        }
    }
    Py_INCREF(op->func_doc);
    return op->func_doc;
}
static int
__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp = op->func_doc;
    if (value == NULL) {
        value = Py_None;
    }
    Py_INCREF(value);
    op->func_doc = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_name == NULL)) {
#if PY_MAJOR_VERSION >= 3
        op->func_name = PyUnicode_InternFromString(op->func.m_ml->ml_name);
#else
        op->func_name = PyString_InternFromString(op->func.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)
{
    PyObject *tmp;
#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;
    }
    tmp = op->func_name;
    Py_INCREF(value);
    op->func_name = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op)
{
    Py_INCREF(op->func_qualname);
    return op->func_qualname;
}
static int
__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
#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;
    }
    tmp = op->func_qualname;
    Py_INCREF(value);
    op->func_qualname = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_self(__pyx_CyFunctionObject *m, CYTHON_UNUSED void *closure)
{
    PyObject *self;
    self = m->func_closure;
    if (self == NULL)
        self = Py_None;
    Py_INCREF(self);
    return self;
}
static PyObject *
__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op)
{
    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)
{
    PyObject *tmp;
    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;
    }
    tmp = op->func_dict;
    Py_INCREF(value);
    op->func_dict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op)
{
    Py_INCREF(op->func_globals);
    return op->func_globals;
}
static PyObject *
__Pyx_CyFunction_get_closure(CYTHON_UNUSED __pyx_CyFunctionObject *op)
{
    Py_INCREF(Py_None);
    return Py_None;
}
static PyObject *
__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op)
{
    PyObject* result = (op->func_code) ? op->func_code : Py_None;
    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_COMPILING_IN_CPYTHON
    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 = PySequence_ITEM(res, 0);
    if (unlikely(!op->defaults_tuple)) result = -1;
    else {
        op->defaults_kwdict = 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) {
    PyObject* tmp;
    if (!value) {
        value = Py_None;
    } else if (value != Py_None && !PyTuple_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__defaults__ must be set to a tuple object");
        return -1;
    }
    Py_INCREF(value);
    tmp = op->defaults_tuple;
    op->defaults_tuple = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_tuple;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (__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) {
    PyObject* tmp;
    if (!value) {
        value = Py_None;
    } else if (value != Py_None && !PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__kwdefaults__ must be set to a dict object");
        return -1;
    }
    Py_INCREF(value);
    tmp = op->defaults_kwdict;
    op->defaults_kwdict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_kwdict;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (__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) {
    PyObject* tmp;
    if (!value || value == Py_None) {
        value = NULL;
    } else if (!PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__annotations__ must be set to a dict object");
        return -1;
    }
    Py_XINCREF(value);
    tmp = op->func_annotations;
    op->func_annotations = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op) {
    PyObject* result = op->func_annotations;
    if (unlikely(!result)) {
        result = PyDict_New();
        if (unlikely(!result)) return NULL;
        op->func_annotations = result;
    }
    Py_INCREF(result);
    return result;
}
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 *) "__self__", (getter)__Pyx_CyFunction_get_self, 0, 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},
    {0, 0, 0, 0, 0}
};
static PyMemberDef __pyx_CyFunction_members[] = {
    {(char *) "__module__", T_OBJECT, offsetof(__pyx_CyFunctionObject, func.m_module), PY_WRITE_RESTRICTED, 0},
    {0, 0, 0,  0, 0}
};
static PyObject *
__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, CYTHON_UNUSED PyObject *args)
{
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromString(m->func.m_ml->ml_name);
#else
    return PyString_FromString(m->func.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
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
#else
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func.m_weakreflist)
#endif
static PyObject *__Pyx_CyFunction_New(PyTypeObject *type, PyMethodDef *ml, int flags, PyObject* qualname,
                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
    __pyx_CyFunctionObject *op = PyObject_GC_New(__pyx_CyFunctionObject, type);
    if (op == NULL)
        return NULL;
    op->flags = flags;
    __Pyx_CyFunction_weakreflist(op) = NULL;
    op->func.m_ml = ml;
    op->func.m_self = (PyObject *) op;
    Py_XINCREF(closure);
    op->func_closure = closure;
    Py_XINCREF(module);
    op->func.m_module = module;
    op->func_dict = NULL;
    op->func_name = NULL;
    Py_INCREF(qualname);
    op->func_qualname = qualname;
    op->func_doc = NULL;
    op->func_classobj = NULL;
    op->func_globals = globals;
    Py_INCREF(op->func_globals);
    Py_XINCREF(code);
    op->func_code = code;
    op->defaults_pyobjects = 0;
    op->defaults = NULL;
    op->defaults_tuple = NULL;
    op->defaults_kwdict = NULL;
    op->defaults_getter = NULL;
    op->func_annotations = NULL;
    PyObject_GC_Track(op);
    return (PyObject *) op;
}
static int
__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
{
    Py_CLEAR(m->func_closure);
    Py_CLEAR(m->func.m_module);
    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);
    Py_CLEAR(m->func_classobj);
    Py_CLEAR(m->defaults_tuple);
    Py_CLEAR(m->defaults_kwdict);
    Py_CLEAR(m->func_annotations);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_XDECREF(pydefaults[i]);
        PyMem_Free(m->defaults);
        m->defaults = NULL;
    }
    return 0;
}
static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    PyObject_GC_UnTrack(m);
    if (__Pyx_CyFunction_weakreflist(m) != NULL)
        PyObject_ClearWeakRefs((PyObject *) m);
    __Pyx_CyFunction_clear(m);
    PyObject_GC_Del(m);
}
static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
{
    Py_VISIT(m->func_closure);
    Py_VISIT(m->func.m_module);
    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);
    Py_VISIT(m->func_classobj);
    Py_VISIT(m->defaults_tuple);
    Py_VISIT(m->defaults_kwdict);
    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_descr_get(PyObject *func, PyObject *obj, PyObject *type)
{
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    if (m->flags & __Pyx_CYFUNCTION_STATICMETHOD) {
        Py_INCREF(func);
        return func;
    }
    if (m->flags & __Pyx_CYFUNCTION_CLASSMETHOD) {
        if (type == NULL)
            type = (PyObject *)(Py_TYPE(obj));
        return __Pyx_PyMethod_New(func, type, (PyObject *)(Py_TYPE(type)));
    }
    if (obj == Py_None)
        obj = NULL;
    return __Pyx_PyMethod_New(func, obj, type);
}
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
}
#if CYTHON_COMPILING_IN_PYPY
static PyObject * __Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyCFunctionObject* f = (PyCFunctionObject*)func;
    PyCFunction meth = f->m_ml->ml_meth;
    PyObject *self = f->m_self;
    Py_ssize_t size;
    switch (f->m_ml->ml_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)meth)(self, arg, kw);
    case METH_NOARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
            size = PyTuple_GET_SIZE(arg);
            if (likely(size == 0))
                return (*meth)(self, NULL);
            PyErr_Format(PyExc_TypeError,
                "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
                f->m_ml->ml_name, size);
            return NULL;
        }
        break;
    case METH_O:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
            size = PyTuple_GET_SIZE(arg);
            if (likely(size == 1)) {
                PyObject *result, *arg0 = PySequence_ITEM(arg, 0);
                if (unlikely(!arg0)) return NULL;
                result = (*meth)(self, arg0);
                Py_DECREF(arg0);
                return result;
            }
            PyErr_Format(PyExc_TypeError,
                "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
                f->m_ml->ml_name, size);
            return NULL;
        }
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags in "
                        "__Pyx_CyFunction_Call. METH_OLDARGS is no "
                        "longer supported!");
        return NULL;
    }
    PyErr_Format(PyExc_TypeError, "%.200s() takes no keyword arguments",
                 f->m_ml->ml_name);
    return NULL;
}
#else
static PyObject * __Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
	return PyCFunction_Call(func, arg, kw);
}
#endif
static PyTypeObject __pyx_CyFunctionType_type = {
    PyVarObject_HEAD_INIT(0, 0)
    "cython_function_or_method",
    sizeof(__pyx_CyFunctionObject),
    0,
    (destructor) __Pyx_CyFunction_dealloc,
    0,
    0,
    0,
#if PY_MAJOR_VERSION < 3
    0,
#else
    0,
#endif
    (reprfunc) __Pyx_CyFunction_repr,
    0,
    0,
    0,
    0,
    __Pyx_CyFunction_Call,
    0,
    0,
    0,
    0,
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,
    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_CyFunction_descr_get,
    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
};
static int __pyx_CyFunction_init(void) {
#if !CYTHON_COMPILING_IN_PYPY
    __pyx_CyFunctionType_type.tp_call = PyCFunction_Call;
#endif
    __pyx_CyFunctionType = __Pyx_FetchCommonType(&__pyx_CyFunctionType_type);
    if (__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 = PyMem_Malloc(size);
    if (!m->defaults)
        return PyErr_NoMemory();
    memset(m->defaults, 0, size);
    m->defaults_pyobjects = pyobjects;
    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);
}

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    #if PY_VERSION_HEX < 0x03030000
    PyObject *py_import;
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
    if (!py_import)
        goto bad;
    #endif
    if (from_list)
        list = from_list;
    else {
        empty_list = PyList_New(0);
        if (!empty_list)
            goto bad;
        list = empty_list;
    }
    global_dict = PyModule_GetDict(__pyx_m);
    if (!global_dict)
        goto bad;
    empty_dict = PyDict_New();
    if (!empty_dict)
        goto bad;
    {
        #if PY_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                #if PY_VERSION_HEX < 0x03030000
                PyObject *py_level = PyInt_FromLong(1);
                if (!py_level)
                    goto bad;
                module = PyObject_CallFunctionObjArgs(py_import,
                    name, global_dict, empty_dict, list, py_level, NULL);
                Py_DECREF(py_level);
                #else
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                #endif
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_VERSION_HEX < 0x03030000
            PyObject *py_level = PyInt_FromLong(level);
            if (!py_level)
                goto bad;
            module = PyObject_CallFunctionObjArgs(py_import,
                name, global_dict, empty_dict, list, py_level, NULL);
            Py_DECREF(py_level);
            #else
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_VERSION_HEX < 0x03030000
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_Format(PyExc_ImportError,
        #if PY_MAJOR_VERSION < 3
            "cannot import name %.230s", PyString_AS_STRING(name));
        #else
            "cannot import name %S", name);
        #endif
    }
    return value;
}

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);
}

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_code = __Pyx_PyCode_New(
        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);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    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;
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    py_frame->f_lineno = py_line;
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_unsigned_int(unsigned int value) {
    const unsigned int neg_one = (unsigned int) -1, const_zero = (unsigned int) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(unsigned int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(unsigned int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(unsigned int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(unsigned int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(unsigned int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(unsigned int),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    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);
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

#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;\
    }

static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *x) {
    const size_t neg_one = (size_t) -1, const_zero = (size_t) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(size_t) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(size_t, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (size_t) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (size_t) 0;
                case  1: __PYX_VERIFY_RETURN_INT(size_t, digit, digits[0])
                case 2:
                    if (8 * sizeof(size_t) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(size_t) >= 2 * PyLong_SHIFT) {
                            return (size_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(size_t) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(size_t) >= 3 * PyLong_SHIFT) {
                            return (size_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(size_t) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_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(size_t) >= 4 * PyLong_SHIFT) {
                            return (size_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
#if CYTHON_COMPILING_IN_CPYTHON
            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 (size_t) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(size_t) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(size_t, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(size_t) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(size_t, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (size_t) 0;
                case -1: __PYX_VERIFY_RETURN_INT(size_t, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(size_t,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(size_t) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) {
                            return (size_t) (((size_t)-1)*(((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(size_t) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) {
                            return (size_t) ((((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) {
                            return (size_t) (((size_t)-1)*(((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(size_t) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) {
                            return (size_t) ((((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_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(size_t) - 1 > 4 * PyLong_SHIFT) {
                            return (size_t) (((size_t)-1)*(((((((((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(size_t) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(size_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(size_t) - 1 > 4 * PyLong_SHIFT) {
                            return (size_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
            if (sizeof(size_t) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(size_t, long, PyLong_AsLong(x))
            } else if (sizeof(size_t) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(size_t, PY_LONG_LONG, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            size_t val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (size_t) -1;
        }
    } else {
        size_t val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (size_t) -1;
        val = __Pyx_PyInt_As_size_t(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to size_t");
    return (size_t) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to size_t");
    return (size_t) -1;
}

static CYTHON_INLINE unsigned int __Pyx_PyInt_As_unsigned_int(PyObject *x) {
    const unsigned int neg_one = (unsigned int) -1, const_zero = (unsigned int) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(unsigned int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(unsigned int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (unsigned int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (unsigned int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(unsigned int, digit, digits[0])
                case 2:
                    if (8 * sizeof(unsigned int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) >= 2 * PyLong_SHIFT) {
                            return (unsigned int) (((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(unsigned int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) >= 3 * PyLong_SHIFT) {
                            return (unsigned int) (((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(unsigned int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned 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(unsigned int) >= 4 * PyLong_SHIFT) {
                            return (unsigned int) (((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            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 (unsigned int) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(unsigned int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(unsigned int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (unsigned int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(unsigned int, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(unsigned int,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(unsigned int) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT) {
                            return (unsigned int) (((unsigned int)-1)*(((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(unsigned int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT) {
                            return (unsigned int) ((((((unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(unsigned int) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT) {
                            return (unsigned int) (((unsigned int)-1)*(((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(unsigned int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT) {
                            return (unsigned int) ((((((((unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(unsigned int) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned 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(unsigned int) - 1 > 4 * PyLong_SHIFT) {
                            return (unsigned int) (((unsigned int)-1)*(((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(unsigned int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned 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(unsigned int) - 1 > 4 * PyLong_SHIFT) {
                            return (unsigned int) ((((((((((unsigned int)digits[3]) << PyLong_SHIFT) | (unsigned int)digits[2]) << PyLong_SHIFT) | (unsigned int)digits[1]) << PyLong_SHIFT) | (unsigned int)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(unsigned int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, long, PyLong_AsLong(x))
            } else if (sizeof(unsigned int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned int, PY_LONG_LONG, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            unsigned int val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (unsigned int) -1;
        }
    } else {
        unsigned int val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (unsigned int) -1;
        val = __Pyx_PyInt_As_unsigned_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to unsigned int");
    return (unsigned int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to unsigned int");
    return (unsigned int) -1;
}

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    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;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
                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
            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))
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
                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))
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        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;
}

#if CYTHON_CCOMPLEX
  #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

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eqf(__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_sumf(__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_difff(__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_prodf(__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;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        float denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__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_zerof(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__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_absf(__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_powf(__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:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(a, a);
                    case 3:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, a);
                    case 4:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_absf(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

#if CYTHON_CCOMPLEX
  #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

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq(__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(__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(__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(__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;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        double denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__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(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__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(__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(__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:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(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

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) {
    const enum NPY_TYPES neg_one = (enum NPY_TYPES) -1, const_zero = (enum NPY_TYPES) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(enum NPY_TYPES) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
        }
    } else {
        if (sizeof(enum NPY_TYPES) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES),
                                     little, !is_unsigned);
    }
}

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    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;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
                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
            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))
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
                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))
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        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;
}

static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

#ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    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;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#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;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling",
            module_name, class_name);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        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);
        }
        #else
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        ++t;
    }
    return 0;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if CYTHON_COMPILING_IN_CPYTHON && (__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)) {
#if PY_VERSION_HEX < 0x03030000
        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
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (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
    } else
#endif
#if (!CYTHON_COMPILING_IN_PYPY) || (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 PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return __Pyx_NewRef(x);
  m = Py_TYPE(x)->tp_as_number;
#if PY_MAJOR_VERSION < 3
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
#else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
#endif
  if (res) {
#if PY_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  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(x);
  }
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    const digit* digits = ((PyLongObject*)b)->ob_digit;
    const Py_ssize_t size = Py_SIZE(b);
    if (likely(__Pyx_sst_abs(size) <= 1)) {
        ival = likely(size) ? digits[0] : 0;
        if (size == -1) ival = -ival;
        return ival;
    } else {
      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 PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
