code: 
  
  
  def 		_A		(		_lowercase				,     _lowercase   )				->   list[list[int]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = []
       __UpperCamelCase   = len(_lowercase   )
       for i in range(_lowercase   ):
            __UpperCamelCase   = []
            for j in range(_lowercase   ):
                 __UpperCamelCase   = 0
                 for k in range(_lowercase   ):
                      __UpperCamelCase   = val + matrix_a[i][k] * matrix_b[k][j]
                 list_a.append(_lowercase   )
            matrix_c.append(_lowercase   )
       return matrix_c
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[int]]:
  
  
       """simple docstring"""
  
  
       return [[int(row == column   ) for column in range(_lowercase   )] for row in range(_lowercase   )]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   int:
  
  
       """simple docstring"""
  
  
       if n <= 1:
            return n
       __UpperCamelCase   = identity(2   )
       __UpperCamelCase   = [[1, 1], [1, 0]]
       __UpperCamelCase   = n - 1
       while n > 0:
            if n % 2 == 1:
                 __UpperCamelCase   = multiply(_lowercase				,     _lowercase   )
            __UpperCamelCase   = multiply(_lowercase				,     _lowercase   )
            __UpperCamelCase   = int(n / 2   )
       return res_matrix[0][0]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   int:
  
  
       """simple docstring"""
  
  
       if n <= 1:
            return n
       __UpperCamelCase   = 0
       __UpperCamelCase   = 1
       for _ in range(2				,     n + 1   ):
            __UpperCamelCase,						__UpperCamelCase   = fiba, fiba + fiba
       return fiba
  
  
  
  
  
  
  def 		_A		(		)				->   None:
  
  
       """simple docstring"""
  
  
       for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
            __UpperCamelCase   = 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(_lowercase   )} and using bruteforce is '''
                f'''{nth_fibonacci_bruteforce(_lowercase   )}\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()
  
  
  
style_context: 
  
  
  from __future__ import annotations
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   int | float:
  
  
       """simple docstring"""
  
  
       if len(_lowercase   ) == 0:
            raise ValueError('find_max() arg is an empty sequence'   )
       __UpperCamelCase   = nums[0]
       for x in nums:
            if x > max_num:
                 __UpperCamelCase   = x
       return max_num
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod(verbose=True)
  
  
  