
'''simple docstring'''
def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      List[Any]            =  []
    snake_case_	:      List[str]            =  len(__SCREAMING_SNAKE_CASE    )
    for i in range(__SCREAMING_SNAKE_CASE    ):
        snake_case_	:      Optional[int]            =  []
        for j in range(__SCREAMING_SNAKE_CASE    ):
            snake_case_	:      Union[str, Any]            =  0
            for k in range(__SCREAMING_SNAKE_CASE    ):
                snake_case_	:      str            =  val + matrix_a[i][k] * matrix_b[k][j]
            list_a.append(__SCREAMING_SNAKE_CASE    )
        matrix_c.append(__SCREAMING_SNAKE_CASE    )
    return matrix_c

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






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

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    if n <= 1:
        return n
    snake_case_	:      int            =  identity(2    )
    snake_case_	:      Tuple            =  [[1, 1], [1, 0]]
    snake_case_	:      Dict            =  n - 1
    while n > 0:
        if n % 2 == 1:
            snake_case_	:      Dict            =  multiply(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )
        snake_case_	:      Union[str, Any]            =  multiply(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    )
        snake_case_	:      List[str]            =  int(n / 2    )
    return res_matrix[0][0]

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    if n <= 1:
        return n
    snake_case_	:      List[Any]            =  0
    snake_case_	:      Any            =  1
    for _ in range(2,						n + 1    ):
        snake_case_     ,	snake_case_	:      List[Any]            =  fiba, fiba + fiba
    return fiba

def   UpperCamelCase_       (		):
    """simple docstring"""






    for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
        snake_case_	:      Dict            =  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(__SCREAMING_SNAKE_CASE    )} and using bruteforce is '
            f'{nth_fibonacci_bruteforce(__SCREAMING_SNAKE_CASE    )}\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()






'''simple docstring'''
def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      Optional[int]            =  len(__SCREAMING_SNAKE_CASE    )

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

    # Continue sorting until the gap is 1
    while gap > 1:
        # Decrease the gap value
        snake_case_	:      Optional[Any]            =  int(gap / shrink    )

        # Sort the elements using insertion sort
        for i in range(__SCREAMING_SNAKE_CASE,						len(__SCREAMING_SNAKE_CASE    )    ):
            snake_case_	:      Any            =  collection[i]
            snake_case_	:      int            =  i
            while j >= gap and collection[j - gap] > temp:
                snake_case_	:      Dict            =  collection[j - gap]
                j -= gap
            snake_case_	:      Optional[int]            =  temp

    return collection


if __name__ == "__main__":
  import doctest

  doctest.testmod()




