/* Generated by Cython 0.24 */

#define PY_SSIZE_T_CLEAN
#include "Python.h"
#ifndef Py_PYTHON_H
    #error Python headers needed to compile C extensions, please install development version of Python.
#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03020000)
    #error Cython requires Python 2.6+ or Python 3.2+.
#else
#define CYTHON_ABI "0_24"
#include <stddef.h>
#ifndef offsetof
  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
#endif
#if !defined(WIN32) && !defined(MS_WINDOWS)
  #ifndef __stdcall
    #define __stdcall
  #endif
  #ifndef __cdecl
    #define __cdecl
  #endif
  #ifndef __fastcall
    #define __fastcall
  #endif
#endif
#ifndef DL_IMPORT
  #define DL_IMPORT(t) t
#endif
#ifndef DL_EXPORT
  #define DL_EXPORT(t) t
#endif
#ifndef PY_LONG_LONG
  #define PY_LONG_LONG LONG_LONG
#endif
#ifndef Py_HUGE_VAL
  #define Py_HUGE_VAL HUGE_VAL
#endif
#ifdef PYPY_VERSION
  #define CYTHON_COMPILING_IN_PYPY 1
  #define CYTHON_COMPILING_IN_CPYTHON 0
#else
  #define CYTHON_COMPILING_IN_PYPY 0
  #define CYTHON_COMPILING_IN_CPYTHON 1
#endif
#if !defined(CYTHON_USE_PYLONG_INTERNALS) && CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x02070000
  #define CYTHON_USE_PYLONG_INTERNALS 1
#endif
#if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
  #undef SHIFT
  #undef BASE
  #undef MASK
#endif
#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
  #define Py_OptimizeFlag 0
#endif
#define __PYX_BUILD_PY_SSIZE_T "n"
#define CYTHON_FORMAT_SSIZE_T "z"
#if PY_MAJOR_VERSION < 3
  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
  #define __Pyx_DefaultClassType PyClass_Type
#else
  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
  #define __Pyx_DefaultClassType PyType_Type
#endif
#ifndef Py_TPFLAGS_CHECKTYPES
  #define Py_TPFLAGS_CHECKTYPES 0
#endif
#ifndef Py_TPFLAGS_HAVE_INDEX
  #define Py_TPFLAGS_HAVE_INDEX 0
#endif
#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
#endif
#ifndef Py_TPFLAGS_HAVE_FINALIZE
  #define Py_TPFLAGS_HAVE_FINALIZE 0
#endif
#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
  #define CYTHON_PEP393_ENABLED 1
  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
                                              0 : _PyUnicode_Ready((PyObject *)(op)))
  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
  #define __Pyx_PyUnicode_KIND(u)         PyUnicode_KIND(u)
  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
#else
  #define CYTHON_PEP393_ENABLED 0
  #define __Pyx_PyUnicode_READY(op)       (0)
  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))
  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))
#endif
#if CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
#else
  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
  #define PyObject_Malloc(s)   PyMem_Malloc(s)
  #define PyObject_Free(p)     PyMem_Free(p)
  #define PyObject_Realloc(p)  PyMem_Realloc(p)
#endif
#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
#else
  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
#endif
#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
  #define PyObject_ASCII(o)            PyObject_Repr(o)
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBaseString_Type            PyUnicode_Type
  #define PyStringObject               PyUnicodeObject
  #define PyString_Type                PyUnicode_Type
  #define PyString_Check               PyUnicode_Check
  #define PyString_CheckExact          PyUnicode_CheckExact
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
#else
  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
#endif
#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
#endif
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#if PY_MAJOR_VERSION >= 3
  #define PyIntObject                  PyLongObject
  #define PyInt_Type                   PyLong_Type
  #define PyInt_Check(op)              PyLong_Check(op)
  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
  #define PyInt_FromString             PyLong_FromString
  #define PyInt_FromUnicode            PyLong_FromUnicode
  #define PyInt_FromLong               PyLong_FromLong
  #define PyInt_FromSize_t             PyLong_FromSize_t
  #define PyInt_FromSsize_t            PyLong_FromSsize_t
  #define PyInt_AsLong                 PyLong_AsLong
  #define PyInt_AS_LONG                PyLong_AS_LONG
  #define PyInt_AsSsize_t              PyLong_AsSsize_t
  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
  #define PyNumber_Int                 PyNumber_Long
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBoolObject                 PyLongObject
#endif
#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
  #ifndef PyUnicode_InternFromString
    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
  #endif
#endif
#if PY_VERSION_HEX < 0x030200A4
  typedef long Py_hash_t;
  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
#else
  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))
#else
  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
#endif
#if PY_VERSION_HEX >= 0x030500B1
#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
#endif
#ifndef CYTHON_RESTRICT
  #if defined(__GNUC__)
    #define CYTHON_RESTRICT __restrict__
  #elif defined(_MSC_VER) && _MSC_VER >= 1400
    #define CYTHON_RESTRICT __restrict
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_RESTRICT restrict
  #else
    #define CYTHON_RESTRICT
  #endif
#endif
#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


#define __PYX_ERR(f_index, lineno, Ln_error) \
{ \
  __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \
}

#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__crosscat__cython_code__State
#define __PYX_HAVE_API__crosscat__cython_code__State
#include <vector>
#include "ios"
#include "new"
#include "stdexcept"
#include "typeinfo"
#include "string.h"
#include <string>
#include <utility>
#include <map>
#include <set>
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "Matrix.h"
#include "State.h"
#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; const char *s; const Py_ssize_t n; const char* encoding;
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;

#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_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_IntOrLong(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
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#else
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
#endif
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(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 PyObject *__pyx_empty_unicode;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

/* None.proto */
#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__)
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":725
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 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
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 * ctypedef npy_int32      int32_t
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typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":726
 * 
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 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":727
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":728
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":732
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":733
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":734
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":735
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":739
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 * ctypedef npy_float64    float64_t
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":740
 * 
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":749
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":750
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":751
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":753
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":755
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":757
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":758
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":760
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":761
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":764
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/* "../../venv-2.7.11-0.1.4/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":766
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck);
#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
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/* ExtTypeTest.proto */
static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);

/* PyIntBinop.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_EqObjC(PyObject *op1, PyObject *op2, long intval, int inplace);
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#define __Pyx_PyInt_EqObjC(op1, op2, intval, inplace)\
    PyObject_RichCompare(op1, op2, Py_EQ)
    #endif

/* PySequenceContains.proto */
static CYTHON_INLINE int __Pyx_PySequence_ContainsTF(PyObject* item, PyObject* seq, int eq) {
    int result = PySequence_Contains(seq, item);
    return unlikely(result < 0) ? result : (result == (eq == Py_EQ));
}

/* ListAppend.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) {
    PyListObject* L = (PyListObject*) list;
    Py_ssize_t len = Py_SIZE(list);
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        Py_INCREF(x);
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#else
#define __Pyx_PyList_Append(L,x) PyList_Append(L,x)
#endif

/* PyObjectLookupSpecial.proto */
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x02070000
static CYTHON_INLINE PyObject* __Pyx_PyObject_LookupSpecial(PyObject* obj, PyObject* attr_name) {
    PyObject *res;
    PyTypeObject *tp = Py_TYPE(obj);
#if PY_MAJOR_VERSION < 3
    if (unlikely(PyInstance_Check(obj)))
        return __Pyx_PyObject_GetAttrStr(obj, attr_name);
#endif
    res = _PyType_Lookup(tp, attr_name);
    if (likely(res)) {
        descrgetfunc f = Py_TYPE(res)->tp_descr_get;
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            Py_INCREF(res);
        } else {
            res = f(res, obj, (PyObject *)tp);
        }
    } else {
        PyErr_SetObject(PyExc_AttributeError, attr_name);
    }
    return res;
}
#else
#define __Pyx_PyObject_LookupSpecial(o,n) __Pyx_PyObject_GetAttrStr(o,n)
#endif

/* GetAttr.proto */
static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *);

/* SaveResetException.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
#else
#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
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/* GetException.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
#endif

/* DictGetItem.proto */
#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
    PyObject *value;
    value = PyDict_GetItemWithError(d, key);
    if (unlikely(!value)) {
        if (!PyErr_Occurred()) {
            PyObject* args = PyTuple_Pack(1, key);
            if (likely(args))
                PyErr_SetObject(PyExc_KeyError, args);
            Py_XDECREF(args);
        }
        return NULL;
    }
    Py_INCREF(value);
    return value;
}
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    #define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key)
#endif

/* PyIntBinop.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace);
#else
#define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace)\
    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
#endif

/* Import.proto */
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);

/* IncludeStringH.proto */
#include <string.h>

/* BytesEquals.proto */
static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);

/* UnicodeEquals.proto */
static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);

/* StrEquals.proto */
#if PY_MAJOR_VERSION >= 3
#define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
#else
#define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
#endif

/* RaiseException.proto */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);

/* RaiseNoneIterError.proto */
static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

/* PyObjectCallMethod0.proto */
static PyObject* __Pyx_PyObject_CallMethod0(PyObject* obj, PyObject* method_name);

/* UnpackTupleError.proto */
static void __Pyx_UnpackTupleError(PyObject *, Py_ssize_t index);

/* UnpackTuple2.proto */
static CYTHON_INLINE int __Pyx_unpack_tuple2(PyObject* tuple, PyObject** value1, PyObject** value2,
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/* dict_iter.proto */
static CYTHON_INLINE PyObject* __Pyx_dict_iterator(PyObject* dict, int is_dict, PyObject* method_name,
                                                   Py_ssize_t* p_orig_length, int* p_is_dict);
static CYTHON_INLINE int __Pyx_dict_iter_next(PyObject* dict_or_iter, Py_ssize_t orig_length, Py_ssize_t* ppos,
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/* CodeObjectCache.proto */
typedef struct {
    PyCodeObject* code_object;
    int code_line;
} __Pyx_CodeObjectCacheEntry;
struct __Pyx_CodeObjectCache {
    int count;
    int max_count;
    __Pyx_CodeObjectCacheEntry* entries;
};
static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static PyCodeObject *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);

/* AddTraceback.proto */
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename);

/* None.proto */
#include <new>

/* BufferStructDeclare.proto */
typedef struct {
  Py_ssize_t shape, strides, suboffsets;
} __Pyx_Buf_DimInfo;
typedef struct {
  size_t refcount;
  Py_buffer pybuffer;
} __Pyx_Buffer;
typedef struct {
  __Pyx_Buffer *rcbuffer;
  char *data;
  __Pyx_Buf_DimInfo diminfo[8];
} __Pyx_LocalBuf_ND;

#if PY_MAJOR_VERSION < 3
    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
    static void __Pyx_ReleaseBuffer(Py_buffer *view);
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    #define __Pyx_GetBuffer PyObject_GetBuffer
    #define __Pyx_ReleaseBuffer PyBuffer_Release
#endif


/* None.proto */
static Py_ssize_t __Pyx_zeros[] = {0, 0, 0, 0, 0, 0, 0, 0};
static Py_ssize_t __Pyx_minusones[] = {-1, -1, -1, -1, -1, -1, -1, -1};

/* CppExceptionConversion.proto */
#ifndef __Pyx_CppExn2PyErr
#include <new>
#include <typeinfo>
#include <stdexcept>
#include <ios>
static void __Pyx_CppExn2PyErr() {
  try {
    if (PyErr_Occurred())
      ; // let the latest Python exn pass through and ignore the current one
    else
      throw;
  } catch (const std::bad_alloc& exn) {
    PyErr_SetString(PyExc_MemoryError, exn.what());
  } catch (const std::bad_cast& exn) {
    PyErr_SetString(PyExc_TypeError, exn.what());
  } catch (const std::domain_error& exn) {
    PyErr_SetString(PyExc_ValueError, exn.what());
  } catch (const std::invalid_argument& exn) {
    PyErr_SetString(PyExc_ValueError, exn.what());
  } catch (const std::ios_base::failure& exn) {
    PyErr_SetString(PyExc_IOError, exn.what());
  } catch (const std::out_of_range& exn) {
    PyErr_SetString(PyExc_IndexError, exn.what());
  } catch (const std::overflow_error& exn) {
    PyErr_SetString(PyExc_OverflowError, exn.what());
  } catch (const std::range_error& exn) {
    PyErr_SetString(PyExc_ArithmeticError, exn.what());
  } catch (const std::underflow_error& exn) {
    PyErr_SetString(PyExc_ArithmeticError, exn.what());
  } catch (const std::exception& exn) {
    PyErr_SetString(PyExc_RuntimeError, exn.what());
  }
  catch (...)
  {
    PyErr_SetString(PyExc_RuntimeError, "Unknown exception");
  }
}
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/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);

/* None.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #define __Pyx_CREAL(z) ((z).real())
    #define __Pyx_CIMAG(z) ((z).imag())
  #else
    #define __Pyx_CREAL(z) (__real__(z))
    #define __Pyx_CIMAG(z) (__imag__(z))
  #endif
#else
    #define __Pyx_CREAL(z) ((z).real)
    #define __Pyx_CIMAG(z) ((z).imag)
#endif
#if defined(__cplusplus) && CYTHON_CCOMPLEX         && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
#else
    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
#endif

/* None.proto */
static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);

/* None.proto */
#if CYTHON_CCOMPLEX
    #define __Pyx_c_eqf(a, b)   ((a)==(b))
    #define __Pyx_c_sumf(a, b)  ((a)+(b))
    #define __Pyx_c_difff(a, b) ((a)-(b))
    #define __Pyx_c_prodf(a, b) ((a)*(b))
    #define __Pyx_c_quotf(a, b) ((a)/(b))
    #define __Pyx_c_negf(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zerof(z) ((z)==(float)0)
    #define __Pyx_c_conjf(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_absf(z)     (::std::abs(z))
        #define __Pyx_c_powf(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zerof(z) ((z)==0)
    #define __Pyx_c_conjf(z)    (conjf(z))
    #if 1
        #define __Pyx_c_absf(z)     (cabsf(z))
        #define __Pyx_c_powf(a, b)  (cpowf(a, b))
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 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex);
    static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex);
    #if 1
        static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex);
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex, __pyx_t_float_complex);
    #endif
#endif

/* None.proto */
static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);

/* None.proto */
#if CYTHON_CCOMPLEX
    #define __Pyx_c_eq(a, b)   ((a)==(b))
    #define __Pyx_c_sum(a, b)  ((a)+(b))
    #define __Pyx_c_diff(a, b) ((a)-(b))
    #define __Pyx_c_prod(a, b) ((a)*(b))
    #define __Pyx_c_quot(a, b) ((a)/(b))
    #define __Pyx_c_neg(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero(z) ((z)==(double)0)
    #define __Pyx_c_conj(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs(z)     (::std::abs(z))
        #define __Pyx_c_pow(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero(z) ((z)==0)
    #define __Pyx_c_conj(z)    (conj(z))
    #if 1
        #define __Pyx_c_abs(z)     (cabs(z))
        #define __Pyx_c_pow(a, b)  (cpow(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex);
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex);
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex, __pyx_t_double_complex);
    #endif
#endif

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value);

/* CIntFromPy.proto */
static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);

/* CIntFromPy.proto */
static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *);

/* CIntFromPy.proto */
static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);

/* CheckBinaryVersion.proto */
static int __Pyx_check_binary_version(void);

/* PyIdentifierFromString.proto */
#if !defined(__Pyx_PyIdentifier_FromString)
#if PY_MAJOR_VERSION < 3
  #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s)
#else
  #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s)
#endif
#endif

/* ModuleImport.proto */
static PyObject *__Pyx_ImportModule(const char *name);

/* TypeImport.proto */
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);

/* InitStrings.proto */
static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);


/* Module declarations from 'libcpp' */

/* Module declarations from 'libcpp.vector' */

/* Module declarations from 'libc.string' */

/* Module declarations from 'libcpp.string' */

/* Module declarations from 'libcpp.utility' */

/* Module declarations from 'libcpp.map' */

/* Module declarations from 'libcpp.set' */

/* Module declarations from 'cpython.buffer' */

/* Module declarations from 'libc.stdio' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.type' */
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;

/* Module declarations from 'cpython' */

/* Module declarations from 'cpython.object' */

/* Module declarations from 'cpython.ref' */

/* Module declarations from 'libc.stdlib' */

/* Module declarations from 'numpy' */

/* Module declarations from 'numpy' */
static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/

/* Module declarations from 'crosscat.cython_code.State' */
static PyTypeObject *__pyx_ptype_8crosscat_11cython_code_5State_p_State = 0;
static std::map<int,std::set<int> >  __pyx_f_8crosscat_11cython_code_5State_empty_map_of_int_set(void); /*proto*/
static double __pyx_f_8crosscat_11cython_code_5State_set_double(double &, double); /*proto*/
static std::vector<int>  __pyx_f_8crosscat_11cython_code_5State_convert_int_vector_to_cpp(PyObject *); /*proto*/
static std::vector<std::string>  __pyx_f_8crosscat_11cython_code_5State_convert_string_vector_to_cpp(PyObject *); /*proto*/
static matrix<double>  *__pyx_f_8crosscat_11cython_code_5State_convert_data_to_cpp(PyArrayObject *); /*proto*/
static std::string __pyx_convert_string_from_py_std__in_string(PyObject *); /*proto*/
static std::vector<double>  __pyx_convert_vector_from_py_double(PyObject *); /*proto*/
static PyObject *__pyx_convert_set_to_py_int(std::set<int>  const &); /*proto*/
static PyObject *__pyx_convert_map_to_py_int____std_3a__3a_set_3c_int_3e___(std::map<int,std::set<int> >  const &); /*proto*/
static std::map<std::string,double>  __pyx_convert_map_from_py_std_3a__3a_string__and_double(PyObject *); /*proto*/
static std::map<int,std::map<std::string,double> >  __pyx_convert_map_from_py_int__and_std_3a__3a_map_3c_std_3a__3a_string_2c_double_3e___(PyObject *); /*proto*/
static std::vector<int>  __pyx_convert_vector_from_py_int(PyObject *); /*proto*/
static std::vector<std::vector<int> >  __pyx_convert_vector_from_py_std_3a__3a_vector_3c_int_3e___(PyObject *); /*proto*/
static std::set<int>  __pyx_convert_set_from_py_int(PyObject *); /*proto*/
static std::map<int,std::set<int> >  __pyx_convert_map_from_py_int__and_std_3a__3a_set_3c_int_3e___(PyObject *); /*proto*/
static std::vector<std::vector<std::vector<int> > >  __pyx_convert_vector_from_py_std_3a__3a_vector_3c_std_3a__3a_vector_3c_int_3e____3e___(PyObject *); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyObject_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyUnicode_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyStr_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyBytes_string_to_py_std__in_string(std::string const &); /*proto*/
static CYTHON_INLINE PyObject *__pyx_convert_PyByteArray_string_to_py_std__in_string(std::string const &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_int(const std::vector<int>  &); /*proto*/
static PyObject *__pyx_convert_map_to_py_int____std_3a__3a_vector_3c_int_3e___(std::map<int,std::vector<int> >  const &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_double(const std::vector<double>  &); /*proto*/
static PyObject *__pyx_convert_map_to_py_std_3a__3a_string____double(std::map<std::string,double>  const &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_std_3a__3a_map_3c_std_3a__3a_string_2c_double_3e___(const std::vector<std::map<std::string,double> >  &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_std_3a__3a_vector_3c_std_3a__3a_map_3c_std_3a__3a_string_2c_double_3e____3e___(const std::vector<std::vector<std::map<std::string,double> > >  &); /*proto*/
static PyObject *__pyx_convert_vector_to_py_std_3a__3a_vector_3c_int_3e___(const std::vector<std::vector<int> >  &); /*proto*/
static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float64_t = { "float64_t", NULL, sizeof(__pyx_t_5numpy_float64_t), { 0 }, 0, 'R', 0, 0 };
#define __Pyx_MODULE_NAME "crosscat.cython_code.State"
int __pyx_module_is_main_crosscat__cython_code__State = 0;

/* Implementation of 'crosscat.cython_code.State' */
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_map;
static PyObject *__pyx_builtin_print;
static PyObject *__pyx_builtin_max;
static PyObject *__pyx_builtin_zip;
static PyObject *__pyx_builtin_enumerate;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_RuntimeError;
static const char __pyx_k_[] = ";";
static const char __pyx_k_T[] = "T";
static const char __pyx_k_c[] = "c";
static const char __pyx_k_r[] = "r";
static const char __pyx_k__2[] = "\n";
static const char __pyx_k__5[] = "";
static const char __pyx_k_fu[] = "fu";
static const char __pyx_k_gu[] = "gu";
static const char __pyx_k_M_c[] = "M_c";
static const char __pyx_k_X_D[] = "X_D";
static const char __pyx_k_X_L[] = "X_L";
static const char __pyx_k__16[] = "*";
static const char __pyx_k_arg[] = "arg";
static const char __pyx_k_dir[] = "dir";
static const char __pyx_k_exp[] = "exp";
static const char __pyx_k_get[] = "get";
static const char __pyx_k_idx[] = "idx";
static const char __pyx_k_key[] = "key";
static const char __pyx_k_map[] = "map";
static const char __pyx_k_max[] = "max";
static const char __pyx_k_six[] = "six";
static const char __pyx_k_zip[] = "zip";
static const char __pyx_k_SEED[] = "SEED";
static const char __pyx_k_exit[] = "__exit__";
static const char __pyx_k_keys[] = "keys";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_seed[] = "seed";
static const char __pyx_k_self[] = "self";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_Timer[] = "Timer";
static const char __pyx_k_alpha[] = "alpha";
static const char __pyx_k_array[] = "array";
static const char __pyx_k_enter[] = "__enter__";
static const char __pyx_k_index[] = "index";
static const char __pyx_k_items[] = "items";
static const char __pyx_k_numpy[] = "numpy";
static const char __pyx_k_print[] = "print";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_timer[] = "timer";
static const char __pyx_k_N_GRID[] = "N_GRID";
static const char __pyx_k_N_keys[] = "N_keys";
static const char __pyx_k_S_GRID[] = "S_GRID";
static const char __pyx_k_counts[] = "counts";
static const char __pyx_k_encode[] = "encode";
static const char __pyx_k_hypers[] = "hypers";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_n_grid[] = "n_grid";
static const char __pyx_k_pickle[] = "pickle";
static const char __pyx_k_random[] = "random";
static const char __pyx_k_update[] = "update";
static const char __pyx_k_MU_GRID[] = "MU_GRID";
static const char __pyx_k_col_idx[] = "col_idx";
static const char __pyx_k_dict_in[] = "dict_in";
static const char __pyx_k_get_X_D[] = "get_X_D";
static const char __pyx_k_get_X_L[] = "get_X_L";
static const char __pyx_k_in_dict[] = "in_dict";
static const char __pyx_k_key_str[] = "key_str";
static const char __pyx_k_n_steps[] = "n_steps";
static const char __pyx_k_nonzero[] = "nonzero";
static const char __pyx_k_row_idx[] = "row_idx";
static const char __pyx_k_verbose[] = "verbose";
static const char __pyx_k_col_name[] = "col_name";
static const char __pyx_k_filename[] = "filename";
static const char __pyx_k_hypers_m[] = "hypers_m";
static const char __pyx_k_join_str[] = "join_str";
static const char __pyx_k_max_time[] = "max_time";
static const char __pyx_k_num_cols[] = "num_cols";
static const char __pyx_k_num_rows[] = "num_rows";
static const char __pyx_k_row_data[] = "row_data";
static const char __pyx_k_step_idx[] = "step_idx";
static const char __pyx_k_view_idx[] = "view_idx";
static const char __pyx_k_CT_KERNEL[] = "CT_KERNEL";
static const char __pyx_k_args_dict[] = "args_dict";
static const char __pyx_k_args_list[] = "args_list";
static const char __pyx_k_ct_kernel[] = "ct_kernel";
static const char __pyx_k_dependent[] = "dependent";
static const char __pyx_k_enumerate[] = "enumerate";
static const char __pyx_k_iteritems[] = "iteritems";
static const char __pyx_k_log_alpha[] = "log_alpha";
static const char __pyx_k_modeltype[] = "modeltype";
static const char __pyx_k_print_str[] = "print_str";
static const char __pyx_k_top_level[] = "top_level";
static const char __pyx_k_vars_dict[] = "vars_dict";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_col_ensure[] = "col_ensure";
static const char __pyx_k_r_not_in_r[] = "%r not in %r";
static const char __pyx_k_transition[] = "transition";
static const char __pyx_k_view_state[] = "view_state";
static const char __pyx_k_which_rows[] = "which_rows";
static const char __pyx_k_RandomState[] = "RandomState";
static const char __pyx_k_State_s_s_s[] = "State[%s, %s]:\n%s";
static const char __pyx_k_assignments[] = "assignments";
static const char __pyx_k_binary_type[] = "binary_type";
static const char __pyx_k_cluster_idx[] = "cluster_idx";
static const char __pyx_k_idx_to_name[] = "idx_to_name";
static const char __pyx_k_independent[] = "independent";
static const char __pyx_k_method_name[] = "method_name";
static const char __pyx_k_name_to_idx[] = "name_to_idx";
static const char __pyx_k_permutation[] = "permutation";
static const char __pyx_k_random_seed[] = "random_seed";
static const char __pyx_k_score_delta[] = "score_delta";
static const char __pyx_k_suffstats_i[] = "suffstats_i";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_column_names[] = "column_names";
static const char __pyx_k_column_types[] = "column_types";
static const char __pyx_k_elapsed_secs[] = "elapsed_secs";
static const char __pyx_k_event_counts[] = "event_counts";
static const char __pyx_k_list_of_list[] = "list_of_list";
static const char __pyx_k_num_clusters[] = "num_clusters";
static const char __pyx_k_random_state[] = "random_state";
static const char __pyx_k_sparsify_X_L[] = "sparsify_X_L";
static const char __pyx_k_view_state_i[] = "view_state_i";
static const char __pyx_k_which_method[] = "which_method";
static const char __pyx_k_column_hypers[] = "column_hypers";
static const char __pyx_k_floatify_dict[] = "floatify_dict";
static const char __pyx_k_get_args_dict[] = "get_args_dict";
static const char __pyx_k_get_num_views[] = "get_num_views";
static const char __pyx_k_value_to_code[] = "value_to_code";
static const char __pyx_k_col_ensure_dep[] = "col_ensure_dep";
static const char __pyx_k_col_ensure_ind[] = "col_ensure_ind";
static const char __pyx_k_col_i_metadata[] = "col_i_metadata";
static const char __pyx_k_desparsify_X_L[] = "desparsify_X_L";
static const char __pyx_k_from_the_prior[] = "from_the_prior";
static const char __pyx_k_get_view_state[] = "get_view_state";
static const char __pyx_k_global_col_idx[] = "global_col_idx";
static const char __pyx_k_indicator_list[] = "indicator_list";
static const char __pyx_k_initialization[] = "initialization";
static const char __pyx_k_max_iterations[] = "max_iterations";
static const char __pyx_k_column_metadata[] = "column_metadata";
static const char __pyx_k_row_crp_alpha_v[] = "row_crp_alpha_v";
static const char __pyx_k_row_partition_v[] = "row_partition_v";
static const char __pyx_k_within_view_idx[] = "within_view_idx";
static const char __pyx_k_column_crp_alpha[] = "column_crp_alpha";
static const char __pyx_k_column_partition[] = "column_partition";
static const char __pyx_k_constructor_args[] = "constructor_args";
static const char __pyx_k_get_elapsed_secs[] = "get_elapsed_secs";
static const char __pyx_k_get_view_state_i[] = "get_view_state_i";
static const char __pyx_k_matching_row_idx[] = "matching_row_idx";
static const char __pyx_k_which_transition[] = "which_transition";
static const char __pyx_k_get_column_hypers[] = "get_column_hypers";
static const char __pyx_k_which_transitions[] = "which_transitions";
static const char __pyx_k_ROW_CRP_ALPHA_GRID[] = "ROW_CRP_ALPHA_GRID";
static const char __pyx_k_floatify_dict_dict[] = "floatify_dict_dict";
static const char __pyx_k_get_col_ensure_dep[] = "get_col_ensure_dep";
static const char __pyx_k_get_col_ensure_ind[] = "get_col_ensure_ind";
static const char __pyx_k_get_column_names_i[] = "get_column_names_i";
static const char __pyx_k_global_col_indices[] = "global_col_indices";
static const char __pyx_k_global_row_indices[] = "global_row_indices";
static const char __pyx_k_insert_zero_values[] = "insert_zero_values";
static const char __pyx_k_row_initialization[] = "row_initialization";
static const char __pyx_k_col_ensure_dep_json[] = "col_ensure_dep_json";
static const char __pyx_k_col_ensure_ind_json[] = "col_ensure_ind_json";
static const char __pyx_k_row_partition_model[] = "row_partition_model";
static const char __pyx_k_transition_features[] = "transition_features";
static const char __pyx_k_without_zero_values[] = "without_zero_values";
static const char __pyx_k_get_column_partition[] = "get_column_partition";
static const char __pyx_k_method_name_and_args[] = "method_name_and_args";
static const char __pyx_k_COLUMN_CRP_ALPHA_GRID[] = "COLUMN_CRP_ALPHA_GRID";
static const char __pyx_k_column_indicator_list[] = "column_indicator_list";
static const char __pyx_k_column_hyperparameters[] = "column_hyperparameters";
static const char __pyx_k_get_modeltype_from_name[] = "get_modeltype_from_name";
static const char __pyx_k_crosscat_utils_file_utils[] = "crosscat.utils.file_utils";
static const char __pyx_k_get_row_partition_model_i[] = "get_row_partition_model_i";
static const char __pyx_k_row_partition_assignments[] = "row_partition_assignments";
static const char __pyx_k_column_component_suffstats[] = "column_component_suffstats";
static const char __pyx_k_crosscat_cython_code_State[] = "crosscat.cython_code.State";
static const char __pyx_k_extract_column_types_counts[] = "extract_column_types_counts";
static const char __pyx_k_extract_row_partition_alpha[] = "extract_row_partition_alpha";
static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static const char __pyx_k_transition_column_crp_alpha[] = "transition_column_crp_alpha";
static const char __pyx_k_column_component_suffstats_i[] = "column_component_suffstats_i";
static const char __pyx_k_column_partition_assignments[] = "column_partition_assignments";
static const char __pyx_k_crosscat_utils_general_utils[] = "crosscat.utils.general_utils";
static const char __pyx_k_get_all_transitions_permuted[] = "get_all_transitions_permuted";
static const char __pyx_k_symmetric_dirichlet_discrete[] = "symmetric_dirichlet_discrete";
static const char __pyx_k_row_partition_hyperparameters[] = "row_partition_hyperparameters";
static const char __pyx_k_indicator_list_to_list_of_list[] = "indicator_list_to_list_of_list";
static const char __pyx_k_Users_probcomp_GoogleDrive_Prob[] = "/Users/probcomp/GoogleDrive/ProbComp/pypi-dist/crosscat/src/cython_code/State.pyx";
static const char __pyx_k_column_partition_hyperparameter[] = "column_partition_hyperparameter";
static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static const char __pyx_k_INVALID_TRANSITION_TYPE_TO_State[] = "INVALID TRANSITION TYPE TO State.transition: %s";
static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static const char __pyx_k_desparsify_column_component_suff[] = "desparsify_column_component_suffstats";
static const char __pyx_k_get_column_component_suffstats_b[] = "get_column_component_suffstats_by_global_col_idx";
static const char __pyx_k_get_column_component_suffstats_i[] = "get_column_component_suffstats_i";
static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static const char __pyx_k_sparsify_column_component_suffst[] = "sparsify_column_component_suffstats";
static const char __pyx_k_transform_latent_state_to_constr[] = "transform_latent_state_to_constructor_args";
static const char __pyx_k_transition_column_hyperparameter[] = "transition_column_hyperparameters";
static const char __pyx_k_transition_name_to_method_name_a[] = "transition_name_to_method_name_and_args";
static const char __pyx_k_transition_row_partition_assignm[] = "transition_row_partition_assignments";
static const char __pyx_k_transition_row_partition_hyperpa[] = "transition_row_partition_hyperparameters";
static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static PyObject *__pyx_kp_b_;
static PyObject *__pyx_n_s_COLUMN_CRP_ALPHA_GRID;
static PyObject *__pyx_n_s_CT_KERNEL;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
static PyObject *__pyx_kp_s_INVALID_TRANSITION_TYPE_TO_State;
static PyObject *__pyx_n_s_MU_GRID;
static PyObject *__pyx_n_s_M_c;
static PyObject *__pyx_n_s_N_GRID;
static PyObject *__pyx_n_s_N_keys;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_ROW_CRP_ALPHA_GRID;
static PyObject *__pyx_n_s_RandomState;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_SEED;
static PyObject *__pyx_n_s_S_GRID;
static PyObject *__pyx_kp_s_State_s_s_s;
static PyObject *__pyx_n_s_T;
static PyObject *__pyx_n_s_Timer;
static PyObject *__pyx_kp_s_Users_probcomp_GoogleDrive_Prob;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s_X_D;
static PyObject *__pyx_n_s_X_L;
static PyObject *__pyx_n_s__16;
static PyObject *__pyx_kp_s__2;
static PyObject *__pyx_kp_s__5;
static PyObject *__pyx_n_s_alpha;
static PyObject *__pyx_n_s_arg;
static PyObject *__pyx_n_s_args_dict;
static PyObject *__pyx_n_s_args_list;
static PyObject *__pyx_n_s_array;
static PyObject *__pyx_n_s_assignments;
static PyObject *__pyx_n_s_binary_type;
static PyObject *__pyx_n_s_c;
static PyObject *__pyx_n_s_cluster_idx;
static PyObject *__pyx_n_s_col_ensure;
static PyObject *__pyx_n_s_col_ensure_dep;
static PyObject *__pyx_n_s_col_ensure_dep_json;
static PyObject *__pyx_n_s_col_ensure_ind;
static PyObject *__pyx_n_s_col_ensure_ind_json;
static PyObject *__pyx_n_s_col_i_metadata;
static PyObject *__pyx_n_s_col_idx;
static PyObject *__pyx_n_s_col_name;
static PyObject *__pyx_n_s_column_component_suffstats;
static PyObject *__pyx_n_s_column_component_suffstats_i;
static PyObject *__pyx_n_s_column_crp_alpha;
static PyObject *__pyx_n_s_column_hyperparameters;
static PyObject *__pyx_n_s_column_hypers;
static PyObject *__pyx_n_s_column_indicator_list;
static PyObject *__pyx_n_s_column_metadata;
static PyObject *__pyx_n_s_column_names;
static PyObject *__pyx_n_s_column_partition;
static PyObject *__pyx_n_s_column_partition_assignments;
static PyObject *__pyx_n_s_column_partition_hyperparameter;
static PyObject *__pyx_n_s_column_types;
static PyObject *__pyx_n_s_constructor_args;
static PyObject *__pyx_n_s_counts;
static PyObject *__pyx_n_s_crosscat_cython_code_State;
static PyObject *__pyx_n_s_crosscat_utils_file_utils;
static PyObject *__pyx_n_s_crosscat_utils_general_utils;
static PyObject *__pyx_n_s_ct_kernel;
static PyObject *__pyx_n_s_dependent;
static PyObject *__pyx_n_s_desparsify_X_L;
static PyObject *__pyx_n_s_desparsify_column_component_suff;
static PyObject *__pyx_n_s_dict_in;
static PyObject *__pyx_n_s_dir;
static PyObject *__pyx_n_s_elapsed_secs;
static PyObject *__pyx_n_s_encode;
static PyObject *__pyx_n_s_enter;
static PyObject *__pyx_n_s_enumerate;
static PyObject *__pyx_n_s_event_counts;
static PyObject *__pyx_n_s_exit;
static PyObject *__pyx_n_s_exp;
static PyObject *__pyx_n_s_extract_column_types_counts;
static PyObject *__pyx_n_s_extract_row_partition_alpha;
static PyObject *__pyx_n_s_filename;
static PyObject *__pyx_n_s_floatify_dict;
static PyObject *__pyx_n_s_floatify_dict_dict;
static PyObject *__pyx_n_s_from_the_prior;
static PyObject *__pyx_n_s_fu;
static PyObject *__pyx_n_s_get;
static PyObject *__pyx_n_s_get_X_D;
static PyObject *__pyx_n_s_get_X_L;
static PyObject *__pyx_n_s_get_all_transitions_permuted;
static PyObject *__pyx_n_s_get_args_dict;
static PyObject *__pyx_n_s_get_col_ensure_dep;
static PyObject *__pyx_n_s_get_col_ensure_ind;
static PyObject *__pyx_n_s_get_column_component_suffstats_b;
static PyObject *__pyx_n_s_get_column_component_suffstats_i;
static PyObject *__pyx_n_s_get_column_hypers;
static PyObject *__pyx_n_s_get_column_names_i;
static PyObject *__pyx_n_s_get_column_partition;
static PyObject *__pyx_n_s_get_elapsed_secs;
static PyObject *__pyx_n_s_get_modeltype_from_name;
static PyObject *__pyx_n_s_get_num_views;
static PyObject *__pyx_n_s_get_row_partition_model_i;
static PyObject *__pyx_n_s_get_view_state;
static PyObject *__pyx_n_s_get_view_state_i;
static PyObject *__pyx_n_s_global_col_idx;
static PyObject *__pyx_n_s_global_col_indices;
static PyObject *__pyx_n_s_global_row_indices;
static PyObject *__pyx_n_s_gu;
static PyObject *__pyx_n_s_hypers;
static PyObject *__pyx_n_s_hypers_m;
static PyObject *__pyx_n_s_idx;
static PyObject *__pyx_n_s_idx_to_name;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_in_dict;
static PyObject *__pyx_n_s_independent;
static PyObject *__pyx_n_s_index;
static PyObject *__pyx_n_s_indicator_list;
static PyObject *__pyx_n_s_indicator_list_to_list_of_list;
static PyObject *__pyx_n_s_initialization;
static PyObject *__pyx_n_s_insert_zero_values;
static PyObject *__pyx_n_s_items;
static PyObject *__pyx_n_s_iteritems;
static PyObject *__pyx_n_s_join_str;
static PyObject *__pyx_n_s_key;
static PyObject *__pyx_n_s_key_str;
static PyObject *__pyx_n_s_keys;
static PyObject *__pyx_n_s_list_of_list;
static PyObject *__pyx_n_s_log_alpha;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_map;
static PyObject *__pyx_n_s_matching_row_idx;
static PyObject *__pyx_n_s_max;
static PyObject *__pyx_n_s_max_iterations;
static PyObject *__pyx_n_s_max_time;
static PyObject *__pyx_n_s_method_name;
static PyObject *__pyx_n_s_method_name_and_args;
static PyObject *__pyx_n_s_modeltype;
static PyObject *__pyx_n_s_n_grid;
static PyObject *__pyx_n_s_n_steps;
static PyObject *__pyx_n_s_name_to_idx;
static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous;
static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou;
static PyObject *__pyx_n_s_nonzero;
static PyObject *__pyx_n_s_num_clusters;
static PyObject *__pyx_n_s_num_cols;
static PyObject *__pyx_n_s_num_rows;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_n_s_permutation;
static PyObject *__pyx_n_s_pickle;
static PyObject *__pyx_n_s_print;
static PyObject *__pyx_n_s_print_str;
static PyObject *__pyx_n_s_r;
static PyObject *__pyx_kp_s_r_not_in_r;
static PyObject *__pyx_n_s_random;
static PyObject *__pyx_n_s_random_seed;
static PyObject *__pyx_n_s_random_state;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_row_crp_alpha_v;
static PyObject *__pyx_n_s_row_data;
static PyObject *__pyx_n_s_row_idx;
static PyObject *__pyx_n_s_row_initialization;
static PyObject *__pyx_n_s_row_partition_assignments;
static PyObject *__pyx_n_s_row_partition_hyperparameters;
static PyObject *__pyx_n_s_row_partition_model;
static PyObject *__pyx_n_s_row_partition_v;
static PyObject *__pyx_n_s_score_delta;
static PyObject *__pyx_n_s_seed;
static PyObject *__pyx_n_s_self;
static PyObject *__pyx_n_s_six;
static PyObject *__pyx_n_s_sparsify_X_L;
static PyObject *__pyx_n_s_sparsify_column_component_suffst;
static PyObject *__pyx_n_s_step_idx;
static PyObject *__pyx_n_s_suffstats_i;
static PyObject *__pyx_n_s_symmetric_dirichlet_discrete;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_timer;
static PyObject *__pyx_n_s_top_level;
static PyObject *__pyx_n_s_transform_latent_state_to_constr;
static PyObject *__pyx_n_s_transition;
static PyObject *__pyx_n_s_transition_column_crp_alpha;
static PyObject *__pyx_n_s_transition_column_hyperparameter;
static PyObject *__pyx_n_s_transition_features;
static PyObject *__pyx_n_s_transition_name_to_method_name_a;
static PyObject *__pyx_n_s_transition_row_partition_assignm;
static PyObject *__pyx_n_s_transition_row_partition_hyperpa;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_update;
static PyObject *__pyx_n_s_value_to_code;
static PyObject *__pyx_n_s_vars_dict;
static PyObject *__pyx_n_s_verbose;
static PyObject *__pyx_n_s_view_idx;
static PyObject *__pyx_n_s_view_state;
static PyObject *__pyx_n_s_view_state_i;
static PyObject *__pyx_n_s_which_method;
static PyObject *__pyx_n_s_which_rows;
static PyObject *__pyx_n_s_which_transition;
static PyObject *__pyx_n_s_which_transitions;
static PyObject *__pyx_n_s_within_view_idx;
static PyObject *__pyx_n_s_without_zero_values;
static PyObject *__pyx_n_s_zip;
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_extract_column_types_counts(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_M_c); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_2get_args_dict(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_args_list, PyObject *__pyx_v_vars_dict); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_4get_all_transitions_permuted(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_seed); /* proto */
static int __pyx_pf_8crosscat_11cython_code_5State_7p_State___cinit__(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_M_c, PyObject *__pyx_v_T, PyObject *__pyx_v_X_L, PyObject *__pyx_v_X_D, PyObject *__pyx_v_initialization, PyObject *__pyx_v_row_initialization, PyObject *__pyx_v_ROW_CRP_ALPHA_GRID, PyObject *__pyx_v_COLUMN_CRP_ALPHA_GRID, PyObject *__pyx_v_S_GRID, PyObject *__pyx_v_MU_GRID, PyObject *__pyx_v_N_GRID, PyObject *__pyx_v_SEED, PyObject *__pyx_v_CT_KERNEL); /* proto */
static void __pyx_pf_8crosscat_11cython_code_5State_7p_State_2__dealloc__(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_4__repr__(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_6to_string(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_join_str, PyObject *__pyx_v_top_level); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_8get_column_groups(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_10get_column_crp_alpha(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_12get_column_crp_score(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_14get_data_score(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_16get_marginal_logp(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_18get_num_views(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_20calc_row_predictive_logp(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_in_vd); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_22get_draw(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_row_idx, PyObject *__pyx_v_random_seed); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_24get_row_partition_model_i(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_view_idx); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_26get_column_names_i(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_view_idx); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_28get_column_component_suffstats_i(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_view_idx); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_30get_view_state_i(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_view_idx); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_32get_column_partition(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_34get_column_hypers(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_36get_view_state(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_38get_col_ensure_dep(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_40get_col_ensure_ind(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_42insert_row(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_row_data, PyObject *__pyx_v_matching_row_idx, PyObject *__pyx_v_row_idx); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_44transition(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_which_transitions, PyObject *__pyx_v_n_steps, PyObject *__pyx_v_c, PyObject *__pyx_v_r, PyObject *__pyx_v_max_iterations, PyObject *__pyx_v_max_time); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_46transition_column_crp_alpha(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_48transition_features(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_c); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_50transition_column_hyperparameters(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_c); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_52transition_row_partition_hyperparameters(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_c); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_54transition_row_partition_assignments(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_r); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_56transition_views(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_58transition_view_i(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_60transition_views_col_hypers(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_62transition_views_row_partition_hyper(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_64transition_views_zs(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_66get_X_D(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_68get_X_L(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_7p_State_70save(struct __pyx_obj_8crosscat_11cython_code_5State_p_State *__pyx_v_self, PyObject *__pyx_v_filename, PyObject *__pyx_v_dir, PyObject *__pyx_v_kwargs); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_6indicator_list_to_list_of_list(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_indicator_list); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_8floatify_dict(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_in_dict); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_10floatify_dict_dict(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_in_dict); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_12extract_row_partition_alpha(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_view_state); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_14transform_latent_state_to_constructor_args(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_X_L, PyObject *__pyx_v_X_D); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_16without_zero_values(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_dict_in); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_18insert_zero_values(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_dict_in, PyObject *__pyx_v_N_keys); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_20sparsify_column_component_suffstats(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_column_component_suffstats); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_22desparsify_column_component_suffstats(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_column_component_suffstats, PyObject *__pyx_v_N_keys); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_24get_column_component_suffstats_by_global_col_idx(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_M_c, PyObject *__pyx_v_X_L, PyObject *__pyx_v_col_idx); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_26sparsify_X_L(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_M_c, PyObject *__pyx_v_X_L); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_28desparsify_X_L(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_M_c, PyObject *__pyx_v_X_L); /* proto */
static PyObject *__pyx_pf_8crosscat_11cython_code_5State_30get_modeltype_from_name(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_M_c, PyObject *__pyx_v_col_name); /* proto */
static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
static PyObject *__pyx_tp_new_8crosscat_11cython_code_5State_p_State(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_float_0_0;
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  #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

/* PyObjectCallNoArg */
    #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

/* BufferFormatCheck */
      static CYTHON_INLINE int __Pyx_IsLittleEndian(void) {
  unsigned int n = 1;
  return *(unsigned char*)(&n) != 0;
}
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case 'B': case 'H': case 'I': case 'L': case 'Q':
        return 'U';
    case 'f': case 'd': case 'g':
        return (is_complex ? 'C' : 'R');
    case 'O':
        return 'O';
    case 'P':
        return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}
static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static CYTHON_INLINE PyObject *
__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
{
    const char *ts = *tsp;
    int i = 0, number;
    int ndim = ctx->head->field->type->ndim;
;
    ++ts;
    if (ctx->new_count != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "Cannot handle repeated arrays in format string");
        return NULL;
    }
    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
    while (*ts && *ts != ')') {
        switch (*ts) {
            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
            default:  break;
        }
        number = __Pyx_BufFmt_ExpectNumber(&ts);
        if (number == -1) return NULL;
        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
            return PyErr_Format(PyExc_ValueError,
                        "Expected a dimension of size %zu, got %d",
                        ctx->head->field->type->arraysize[i], number);
        if (*ts != ',' && *ts != ')')
            return PyErr_Format(PyExc_ValueError,
                                "Expected a comma in format string, got '%c'", *ts);
        if (*ts == ',') ts++;
        i++;
    }
    if (i != ndim)
        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                            ctx->head->field->type->ndim, i);
    if (!*ts) {
        PyErr_SetString(PyExc_ValueError,
                        "Unexpected end of format string, expected ')'");
        return NULL;
    }
    ctx->is_valid_array = 1;
    ctx->new_count = 1;
    *tsp = ++ts;
    return Py_None;
}
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case '\r':
      case '\n':
        ++ts;
        break;
      case '<':
        if (!__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        ctx->new_packmode = *ts++;
        break;
      case 'T':
        {
          const char* ts_after_sub;
          size_t i, struct_count = ctx->new_count;
          size_t struct_alignment = ctx->struct_alignment;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          ctx->enc_count = 0;
          ctx->struct_alignment = 0;
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
          if (struct_alignment) ctx->struct_alignment = struct_alignment;
        }
        break;
      case '}':
        {
          size_t alignment = ctx->struct_alignment;
          ++ts;
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          if (alignment && ctx->fmt_offset % alignment) {
            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
          }
        }
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ctx->enc_packmode = ctx->new_packmode;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }
      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O': case 'p':
        if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
            ctx->enc_packmode == ctx->new_packmode) {
          ctx->enc_count += ctx->new_count;
          ctx->new_count = 1;
          got_Z = 0;
          ++ts;
          break;
        }
      case 's':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->enc_count = ctx->new_count;
        ctx->enc_packmode = ctx->new_packmode;
        ctx->enc_type = *ts;
        ctx->is_complex = got_Z;
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      case ':':
        ++ts;
        while(*ts != ':') ++ts;
        ++ts;
        break;
      case '(':
        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
        break;
      default:
        {
          int number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          ctx->new_count = (size_t)number;
        }
    }
  }
}
static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) {
  buf->buf = NULL;
  buf->obj = NULL;
  buf->strides = __Pyx_zeros;
  buf->shape = __Pyx_zeros;
  buf->suboffsets = __Pyx_minusones;
}
static CYTHON_INLINE int __Pyx_GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  if (obj == Py_None || obj == NULL) {
    __Pyx_ZeroBuffer(buf);
    return 0;
  }
  buf->buf = NULL;
  if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
  if (buf->ndim != nd) {
    PyErr_Format(PyExc_ValueError,
                 "Buffer has wrong number of dimensions (expected %d, got %d)",
                 nd, buf->ndim);
    goto fail;
  }
  if (!cast) {
    __Pyx_BufFmt_Context ctx;
    __Pyx_BufFmt_Init(&ctx, stack, dtype);
    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
  }
  if ((unsigned)buf->itemsize != dtype->size) {
    PyErr_Format(PyExc_ValueError,
      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
    goto fail;
  }
  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
  return 0;
fail:;
  __Pyx_ZeroBuffer(buf);
  return -1;
}
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (info->buf == NULL) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}

/* BufferIndexError */
        static void __Pyx_RaiseBufferIndexError(int axis) {
  PyErr_Format(PyExc_IndexError,
     "Out of bounds on buffer access (axis %d)", axis);
}

/* RaiseArgTupleInvalid */
        static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

/* RaiseDoubleKeywords */
        static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}

/* ParseKeywords */
        static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

/* RaiseTooManyValuesToUnpack */
        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);
}

/* RaiseNeedMoreValuesToUnpack */
        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");
}

/* IterFinish */
        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
}

/* UnpackItemEndCheck */
        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;
}

/* GetItemInt */
        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))
                        return NULL;
                    PyErr_Clear();
                }
            }
            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));
}

/* ExtTypeTest */
        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;
}

/* PyIntBinop */
        #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

/* GetAttr */
        static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) {
#if CYTHON_COMPILING_IN_CPYTHON
#if PY_MAJOR_VERSION >= 3
    if (likely(PyUnicode_Check(n)))
#else
    if (likely(PyString_Check(n)))
#endif
        return __Pyx_PyObject_GetAttrStr(o, n);
#endif
    return PyObject_GetAttr(o, n);
}

/* SaveResetException */
        #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
#endif

/* GetException */
        #if CYTHON_COMPILING_IN_CPYTHON
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
#endif
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_COMPILING_IN_CPYTHON
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
    #endif
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

/* PyIntBinop */
          #if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = (long)((unsigned long)a + b);
            if (likely((x^a) >= 0 || (x^b) >= 0))
                return PyInt_FromLong(x);
            return PyLong_Type.tp_as_number->nb_add(op1, op2);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS && PY_MAJOR_VERSION >= 3
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
        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;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                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;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                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;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                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;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                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;
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
                    }
                default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
            }
        }
                x = a + b;
            return PyLong_FromLong(x);
        long_long:
                llx = lla + llb;
            return PyLong_FromLongLong(llx);
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            double result;
            PyFPE_START_PROTECT("add", return NULL)
            result = ((double)a) + (double)b;
            PyFPE_END_PROTECT(result)
            return PyFloat_FromDouble(result);
    }
    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
}
#endif

/* Import */
          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;
}

/* BytesEquals */
          static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

/* UnicodeEquals */
          static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
#if PY_MAJOR_VERSION < 3
    PyObject* owned_ref = NULL;
#endif
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
#if PY_MAJOR_VERSION < 3
    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
        owned_ref = PyUnicode_FromObject(s2);
        if (unlikely(!owned_ref))
            return -1;
        s2 = owned_ref;
        s2_is_unicode = 1;
    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
        owned_ref = PyUnicode_FromObject(s1);
        if (unlikely(!owned_ref))
            return -1;
        s1 = owned_ref;
        s1_is_unicode = 1;
    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
        return __Pyx_PyBytes_Equals(s1, s2, equals);
    }
#endif
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length;
        int kind;
        void *data1, *data2;
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
            goto return_ne;
        }
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            #if PY_MAJOR_VERSION < 3
            Py_XDECREF(owned_ref);
            #endif
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_EQ);
return_ne:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_NE);
#endif
}

/* RaiseException */
          #if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *cause) {
    __Pyx_PyThreadState_declare
    Py_XINCREF(type);
    if (!value || value == Py_None)
        value = NULL;
    else
        Py_INCREF(value);
    if (!tb || tb == Py_None)
        tb = NULL;
    else {
        Py_INCREF(tb);
        if (!PyTraceBack_Check(tb)) {
            PyErr_SetString(PyExc_TypeError,
                "raise: arg 3 must be a traceback or None");
            goto raise_error;
        }
    }
    if (PyType_Check(type)) {
#if CYTHON_COMPILING_IN_PYPY
        if (!value) {
            Py_INCREF(Py_None);
            value = Py_None;
        }
#endif
        PyErr_NormalizeException(&type, &value, &tb);
    } else {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        value = type;
        type = (PyObject*) Py_TYPE(type);
        Py_INCREF(type);
        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
            PyErr_SetString(PyExc_TypeError,
                "raise: exception class must be a subclass of BaseException");
            goto raise_error;
        }
    }
    __Pyx_PyThreadState_assign
    __Pyx_ErrRestore(type, value, tb);
    return;
raise_error:
    Py_XDECREF(value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
    return;
}
#else
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
    PyObject* owned_instance = NULL;
    if (tb == Py_None) {
        tb = 0;
    } else if (tb && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto bad;
    }
    if (value == Py_None)
        value = 0;
    if (PyExceptionInstance_Check(type)) {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto bad;
        }
        value = type;
        type = (PyObject*) Py_TYPE(value);
    } else if (PyExceptionClass_Check(type)) {
        PyObject *instance_class = NULL;
        if (value && PyExceptionInstance_Check(value)) {
            instance_class = (PyObject*) Py_TYPE(value);
            if (instance_class != type) {
                int is_subclass = PyObject_IsSubclass(instance_class, type);
                if (!is_subclass) {
                    instance_class = NULL;
                } else if (unlikely(is_subclass == -1)) {
                    goto bad;
                } else {
                    type = instance_class;
                }
            }
        }
        if (!instance_class) {
            PyObject *args;
            if (!value)
                args = PyTuple_New(0);
            else if (PyTuple_Check(value)) {
                Py_INCREF(value);
                args = value;
            } else
                args = PyTuple_Pack(1, value);
            if (!args)
                goto bad;
            owned_instance = PyObject_Call(type, args, NULL);
            Py_DECREF(args);
            if (!owned_instance)
                goto bad;
            value = owned_instance;
            if (!PyExceptionInstance_Check(value)) {
                PyErr_Format(PyExc_TypeError,
                             "calling %R should have returned an instance of "
                             "BaseException, not %R",
                             type, Py_TYPE(value));
                goto bad;
            }
        }
    } else {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
#if 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

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

/* PyObjectCallMethod0 */
            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;
}

/* UnpackTupleError */
            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);
    }
}

/* UnpackTuple2 */
            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;
}

/* dict_iter */
            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;
}

/* CodeObjectCache */
            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);
}

/* AddTraceback */
            #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);
}

#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
    return -1;
}
static void __Pyx_ReleaseBuffer(Py_buffer *view) {
    PyObject *obj = view->obj;
    if (!obj) return;
    if (PyObject_CheckBuffer(obj)) {
        PyBuffer_Release(view);
        return;
    }
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; }
    Py_DECREF(obj);
    view->obj = NULL;
}
#endif


            /* CIntFromPyVerify */
            #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

/* CIntToPy */
            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);
    }
}

/* CIntToPy */
            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);
    }
}

/* None */
            #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

/* None */
            #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

/* None */
            #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

/* None */
            #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

/* CIntToPy */
            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);
    }
}

/* CIntFromPy */
            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_IntOrLong(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_IntOrLong(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;
}

/* CIntFromPy */
            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_IntOrLong(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_IntOrLong(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;
}

/* CIntFromPy */
            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_IntOrLong(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_IntOrLong(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;
}

/* CheckBinaryVersion */
            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;
}

/* ModuleImport */
            #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

/* TypeImport */
            #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. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        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. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

/* InitStrings */
            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_IntOrLong(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 */
