



def 						UpperCAmelCase__   (   UpperCAmelCase__			:list[list[int]]			,       UpperCAmelCase__			:list[list[int]]       ):






 '''simple docstring'''

 a							=		[]
 a							=		len(UpperCAmelCase__       )
 for i in range(UpperCAmelCase__       ):
  a							=		[]
  for j in range(UpperCAmelCase__       ):
   a							=		0
   for k in range(UpperCAmelCase__       ):
    a							=		val + matrix_a[i][k] * matrix_b[k][j]
   list_a.append(UpperCAmelCase__       )
  matrix_c.append(UpperCAmelCase__       )
 return matrix_c


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 return [[int(row == column       ) for column in range(UpperCAmelCase__       )] for row in range(UpperCAmelCase__       )]


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 if n <= 1:
  return n
 a							=		identity(2       )
 a							=		[[1, 1], [1, 0]]
 a							=		n - 1
 while n > 0:
  if n % 2 == 1:
   a							=		multiply(UpperCAmelCase__			,       UpperCAmelCase__       )
  a							=		multiply(UpperCAmelCase__			,       UpperCAmelCase__       )
  a							=		int(n / 2       )
 return res_matrix[0][0]


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 if n <= 1:
  return n
 a							=		0
 a							=		1
 for _ in range(2			,       n + 1       ):
  a		,	a							=		fiba, fiba + fiba
 return fiba


def 						UpperCAmelCase__   (   ):






 '''simple docstring'''

 for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
  a							=		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(UpperCAmelCase__       )} and using bruteforce is """
      F"""{nth_fibonacci_bruteforce(UpperCAmelCase__       )}\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()






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


A_		:  Any										=  {
    '''configuration_align''': [
        '''ALIGN_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''AlignConfig''',
        '''AlignTextConfig''',
        '''AlignVisionConfig''',
    ],
    '''processing_align''': ['''AlignProcessor'''],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     A_		:  Optional[int]										=  [
         '''ALIGN_PRETRAINED_MODEL_ARCHIVE_LIST''',
         '''AlignModel''',
         '''AlignPreTrainedModel''',
         '''AlignTextModel''',
         '''AlignVisionModel''',
     ]

if TYPE_CHECKING:
     from .configuration_align import (
         ALIGN_PRETRAINED_CONFIG_ARCHIVE_MAP,
         AlignConfig,
         AlignTextConfig,
         AlignVisionConfig,
     )
     from .processing_align import AlignProcessor

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_align import (
              ALIGN_PRETRAINED_MODEL_ARCHIVE_LIST,
              AlignModel,
              AlignPreTrainedModel,
              AlignTextModel,
              AlignVisionModel,
          )

else:
     import sys

     A_		:  int										=  _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

