"""simple docstring"""
def  lowerCAmelCase__     (      _UpperCamelCase							:					list[list[int]]			,      _UpperCamelCase							:					list[list[int]]       )       ->					list[list[int]]:





						"""simple docstring"""






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





def  lowerCAmelCase__     (      _UpperCamelCase							:					int       )       ->					list[list[int]]:





						"""simple docstring"""






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





def  lowerCAmelCase__     (      _UpperCamelCase							:					int       )       ->					int:





						"""simple docstring"""






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





def  lowerCAmelCase__     (      _UpperCamelCase							:					int       )       ->					int:





						"""simple docstring"""






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





def  lowerCAmelCase__     (      )       ->					None:





						"""simple docstring"""






						for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
												snake_case             =      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()





def      a__	(						UpperCAmelCase				:     list     )    ->		list:
  UpperCAmelCase			:				Tuple										=					len(UpperCAmelCase     )

  # Set the gap value to be decreased by a factor of 1.3
  # after each iteration
  UpperCAmelCase			:				Optional[Any]										=					1.3

  # Continue sorting until the gap is 1
  while gap > 1:
    # Decrease the gap value
    UpperCAmelCase			:				int										=					int(gap / shrink     )

    # Sort the elements using insertion sort
    for i in range(UpperCAmelCase							,					len(UpperCAmelCase     )     ):
      UpperCAmelCase			:				Union[str, Any]										=					collection[i]
      UpperCAmelCase			:				List[Any]										=					i
      while j >= gap and collection[j - gap] > temp:
        UpperCAmelCase			:				int										=					collection[j - gap]
        j -= gap
      UpperCAmelCase			:				List[Any]										=					temp

  return collection


if __name__ == "__main__":
     import doctest

     doctest.testmod()





