
def       UpperCAmelCase_					(  __lowerCAmelCase		,   __lowerCAmelCase		)	->  list[list[int]]:
    __lowercase						:     str		      =    []
    __lowercase						:     int		      =    len(__lowerCAmelCase		)
    for i in range(__lowerCAmelCase		):
        __lowercase						:     str		      =    []
        for j in range(__lowerCAmelCase		):
            __lowercase						:     str		      =    0
            for k in range(__lowerCAmelCase		):
                __lowercase						:     List[str]		      =    val + matrix_a[i][k] * matrix_b[k][j]
            list_a.append(__lowerCAmelCase		)
        matrix_c.append(__lowerCAmelCase		)
    return matrix_c


def       UpperCAmelCase_					(  __lowerCAmelCase		)	->  list[list[int]]:
    return [[int(row == column		) for column in range(__lowerCAmelCase		)] for row in range(__lowerCAmelCase		)]


def       UpperCAmelCase_					(  __lowerCAmelCase		)	->  int:
    if n <= 1:
        return n
    __lowercase						:     Optional[Any]		      =    identity(2		)
    __lowercase						:     Union[str, Any]		      =    [[1, 1], [1, 0]]
    __lowercase						:     str		      =    n - 1
    while n > 0:
        if n % 2 == 1:
            __lowercase						:     Tuple		      =    multiply(__lowerCAmelCase		,   __lowerCAmelCase		)
        __lowercase						:     List[str]		      =    multiply(__lowerCAmelCase		,   __lowerCAmelCase		)
        __lowercase						:     List[Any]		      =    int(n / 2		)
    return res_matrix[0][0]


def       UpperCAmelCase_					(  __lowerCAmelCase		)	->  int:
    if n <= 1:
        return n
    __lowercase						:     str		      =    0
    __lowercase						:     str		      =    1
    for _ in range(2		,   n + 1		):
        __lowercase      , __lowercase						:     Optional[int]		      =    fiba, fiba + fiba
    return fiba


def       UpperCAmelCase_					(  )	->  None:
    for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
        __lowercase						:     Optional[Any]		      =    int(''''''.join(c for c in ordinal if c in '''0123456789'''		)		)  # 1000th --> 1000
        print(
            F'{ordinal} fibonacci number using matrix exponentiation is '
            F'{nth_fibonacci_matrix(__lowerCAmelCase		)} and using bruteforce is '
            F'{nth_fibonacci_bruteforce(__lowerCAmelCase		)}\n'		)
    # from timeit import timeit
    # print(timeit("nth_fibonacci_matrix(1000000)",
    #              "from main import nth_fibonacci_matrix", number=5))
    # print(timeit("nth_fibonacci_bruteforce(1000000)",
    #              "from main import nth_fibonacci_bruteforce", number=5))
    # 2.3342058970001744
    # 57.256506615000035


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()




import importlib.metadata
import sys

from transformers.testing_utils import TestCasePlus
from transformers.utils.versions import require_version, require_version_core


__lowerCAmelCase   :     Optional[Any]      =						importlib.metadata.version("numpy")
__lowerCAmelCase   :     Any      =						".".join([str(x) for x in sys.version_info[:3]])


class   __lowerCAmelCase		(		lowerCAmelCase_ ):



      """simple docstring"""







      def 						snake_case_     ( self						:    List[Any]			):
          # lt + different version strings
          require_version_core('''numpy<1000.4.5'''			)
          require_version_core('''numpy<1000.4'''			)
          require_version_core('''numpy<1000'''			)

          # le
          require_version_core('''numpy<=1000.4.5'''			)
          require_version_core(F'numpy<={numpy_ver}'			)

          # eq
          require_version_core(F'numpy=={numpy_ver}'			)

          # ne
          require_version_core('''numpy!=1000.4.5'''			)

          # ge
          require_version_core('''numpy>=1.0'''			)
          require_version_core('''numpy>=1.0.0'''			)
          require_version_core(F'numpy>={numpy_ver}'			)

          # gt
          require_version_core('''numpy>1.0.0'''			)

          # mix
          require_version_core('''numpy>1.0.0,<1000'''			)

          # requirement w/o version
          require_version_core('''numpy'''			)

          # unmet requirements due to version conflict
          for req in ["numpy==1.0.0", "numpy>=1000.0.0", F'numpy<{numpy_ver}']:
              try:
                  require_version_core(_snake_case			)
              except ImportError as e:
                  self.assertIn(F'{req} is required'			,    str(_snake_case			)			)
                  self.assertIn('''but found'''			,    str(_snake_case			)			)

        # unmet requirements due to missing module
          for req in ["numpipypie>1", "numpipypie2"]:
              try:
                  require_version_core(_snake_case			)
              except importlib.metadata.PackageNotFoundError as e:
                  self.assertIn(F'The \'{req}\' distribution was not found and is required by this application'			,    str(_snake_case			)			)
                  self.assertIn('''Try: pip install transformers -U'''			,    str(_snake_case			)			)

        # bogus requirements formats:
        # 1. whole thing
          for req in ["numpy??1.0.0", "numpy1.0.0"]:
              try:
                  require_version_core(_snake_case			)
              except ValueError as e:
                  self.assertIn('''requirement needs to be in the pip package format'''			,    str(_snake_case			)			)
        # 2. only operators
          for req in ["numpy=1.0.0", "numpy == 1.00", "numpy<>1.0.0", "numpy><1.00", "numpy>>1.0.0"]:
              try:
                  require_version_core(_snake_case			)
              except ValueError as e:
                  self.assertIn('''need one of '''			,    str(_snake_case			)			)




      def 						snake_case_     ( self						:    List[str]			):
          # matching requirement
          require_version('''python>=3.6.0'''			)

          # not matching requirements
          for req in ["python>9.9.9", "python<3.0.0"]:
              try:
                  require_version_core(_snake_case			)
              except ImportError as e:
                  self.assertIn(F'{req} is required'			,    str(_snake_case			)			)
                  self.assertIn(F'but found python=={python_ver}'			,    str(_snake_case			)			)


