




'''simple docstring'''




def     snake_case__     (			lowerCamelCase__					: int      ) -> int:
					if not isinstance(_UpperCamelCase      ,		_UpperCamelCase      ):
										A_			:  List[Any]			=				f'Input value of [number={number}] must be an integer'
										raise TypeError(_UpperCamelCase      )
					if number < 1:
										raise ValueError('''Input must be a positive integer'''      )
					return number * (2 * number - 1)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




'''simple docstring'''




def 	_UpperCAmelCase       (				_UpperCamelCase       :      list[list[int]],  _UpperCamelCase       :      list[list[int]]  )      -> list[list[int]]:
    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  )      -> list[list[int]]:
    return [[int(row == column  ) for column in range(_UpperCamelCase  )] for row in range(_UpperCamelCase  )]





def 	_UpperCAmelCase       (				_UpperCamelCase       :      int  )      -> int:
    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  )      -> int:
    if n <= 1:
        return n
    A_      =  0
    A_      =  1
    for _ in range(2,  n + 1  ):
        A_  ,A_      =  fiba, fiba + fiba
    return fiba





def 	_UpperCAmelCase       (				)      -> None:
    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()






