from __future__ import annotations

import math






def  snake_case  (       snake_case__			:list   ,	snake_case__			:list)						->   list:
       if len(snake_case__) != 2 or len(a[0]) != 2 or len(snake_case__) != 2 or len(b[0]) != 2:
              raise Exception("""Matrices are not 2x2""")
       _A        =  [
           [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
           [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
       ]
       return new_matrix






def  snake_case  (       snake_case__			:list   ,	snake_case__			:list)						->   List[str]:
       return [
           [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]))]
           for row in range(len(snake_case__))
       ]






def  snake_case  (       snake_case__			:list   ,	snake_case__			:list)						->   int:
       return [
           [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]))]
           for row in range(len(snake_case__))
       ]






def  snake_case  (       snake_case__			:list)						->   tuple[list, list, list, list]:
       if len(snake_case__) % 2 != 0 or len(a[0]) % 2 != 0:
              raise Exception("""Odd matrices are not supported!""")

       _A        =  len(snake_case__)
       _A        =  matrix_length // 2

       _A        =  [[a[i][j] for j in range(snake_case__   ,	snake_case__)] for i in range(snake_case__)]
       _A        =  [
           [a[i][j] for j in range(snake_case__   ,	snake_case__)] for i in range(snake_case__   ,	snake_case__)
       ]

       _A        =  [[a[i][j] for j in range(snake_case__)] for i in range(snake_case__)]
       _A        =  [[a[i][j] for j in range(snake_case__)] for i in range(snake_case__   ,	snake_case__)]

       return top_left, top_right, bot_left, bot_right






def  snake_case  (       snake_case__			:list)						->   tuple[int, int]:
       return len(snake_case__), len(matrix[0])






def  snake_case  (       snake_case__			:list)						->   None:
       print("""\n""".join(str(snake_case__) for line in matrix))






def  snake_case  (       snake_case__			:list   ,	snake_case__			:list)						->   list:
       if matrix_dimensions(snake_case__) == (2, 2):
              return default_matrix_multiplication(snake_case__   ,	snake_case__)

       _A   ,  _A   ,  _A   ,  _A        =  split_matrix(snake_case__)
       _A   ,  _A   ,  _A   ,  _A        =  split_matrix(snake_case__)

       _A        =  actual_strassen(snake_case__   ,	matrix_subtraction(snake_case__   ,	snake_case__))
       _A        =  actual_strassen(matrix_addition(snake_case__   ,	snake_case__)   ,	snake_case__)
       _A        =  actual_strassen(matrix_addition(snake_case__   ,	snake_case__)   ,	snake_case__)
       _A        =  actual_strassen(snake_case__   ,	matrix_subtraction(snake_case__   ,	snake_case__))
       _A        =  actual_strassen(matrix_addition(snake_case__   ,	snake_case__)   ,	matrix_addition(snake_case__   ,	snake_case__))
       _A        =  actual_strassen(matrix_subtraction(snake_case__   ,	snake_case__)   ,	matrix_addition(snake_case__   ,	snake_case__))
       _A        =  actual_strassen(matrix_subtraction(snake_case__   ,	snake_case__)   ,	matrix_addition(snake_case__   ,	snake_case__))

       _A        =  matrix_addition(matrix_subtraction(matrix_addition(snake_case__   ,	snake_case__)   ,	snake_case__)   ,	snake_case__)
       _A        =  matrix_addition(snake_case__   ,	snake_case__)
       _A        =  matrix_addition(snake_case__   ,	snake_case__)
       _A        =  matrix_subtraction(matrix_subtraction(matrix_addition(snake_case__   ,	snake_case__)   ,	snake_case__)   ,	snake_case__)

       # construct the new matrix from our 4 quadrants
       _A        =  []
       for i in range(len(snake_case__)):
              new_matrix.append(top_left[i] + top_right[i])
       for i in range(len(snake_case__)):
              new_matrix.append(bot_left[i] + bot_right[i])
       return new_matrix






def  snake_case  (       snake_case__			:list   ,	snake_case__			:list)						->   list:
       if matrix_dimensions(snake_case__)[1] != matrix_dimensions(snake_case__)[0]:
              _A        =  (
                  """Unable to multiply these matrices, please check the dimensions.\n"""
                  F'''Matrix A: {matrixa}\n'''
                  F'''Matrix B: {matrixa}'''
              )
              raise Exception(snake_case__)
       _A        =  matrix_dimensions(snake_case__)
       _A        =  matrix_dimensions(snake_case__)

       if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
              return [matrixa, matrixa]

       _A        =  max(*snake_case__   ,	*snake_case__)
       _A        =  int(math.pow(2   ,	math.ceil(math.loga(snake_case__))))
       _A        =  matrixa
       _A        =  matrixa

       # Adding zeros to the matrices so that the arrays dimensions are the same and also
       # power of 2
       for i in range(0   ,	snake_case__):
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]   ,	snake_case__):
                            new_matrixa[i].append(0)
              else:
                     new_matrixa.append([0] * maxim)
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]   ,	snake_case__):
                            new_matrixa[i].append(0)
              else:
                     new_matrixa.append([0] * maxim)

       _A        =  actual_strassen(snake_case__   ,	snake_case__)

       # Removing the additional zeros
       for i in range(0   ,	snake_case__):
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]   ,	snake_case__):
                            final_matrix[i].pop()
              else:
                     final_matrix.pop()
       return final_matrix


if __name__ == "__main__":
    _SCREAMING_SNAKE_CASE										=						[
        [2, 3, 4, 5],
        [6, 4, 3, 1],
        [2, 3, 6, 7],
        [3, 1, 2, 4],
        [2, 3, 4, 5],
        [6, 4, 3, 1],
        [2, 3, 6, 7],
        [3, 1, 2, 4],
        [2, 3, 4, 5],
        [6, 2, 3, 1],
    ]
    _SCREAMING_SNAKE_CASE										=						[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
    print(strassen(matrixa, matrixa))





from math import isqrt






def  snake_case  (       snake_case__			:int)						->   bool:
       return all(number % divisor != 0 for divisor in range(2   ,	isqrt(snake_case__) + 1))






def  snake_case  (       snake_case__			:int = 10**6)						->   int:
       _A        =  0
       _A        =  1
       _A        =  7
       while prime_candidate < max_prime:
              primes_count += is_prime(snake_case__)

              cube_index += 1
              prime_candidate += 6 * cube_index

       return primes_count


if __name__ == "__main__":
    print(F'''{solution() = }''')




