

from __future__ import annotations

import math





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							if len(UpperCamelCase__ ) != 2 or len(a[0] ) != 2 or len(UpperCamelCase__ ) != 2 or len(b[0] ) != 2:
														raise Exception('Matrices are not 2x2' )
							snake_case_     							=       [
							    [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    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							return [
							    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row] ) )]
							    for row in range(len(UpperCamelCase__ ) )
							]





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							return [
							    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row] ) )]
							    for row in range(len(UpperCamelCase__ ) )
							]





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''simple docstring'''






							if len(UpperCamelCase__ ) % 2 != 0 or len(a[0] ) % 2 != 0:
														raise Exception('Odd matrices are not supported!' )

							snake_case_     							=       len(UpperCamelCase__ )
							snake_case_     							=       matrix_length // 2

							snake_case_     							=       [[a[i][j] for j in range(UpperCamelCase__  ,				UpperCamelCase__ )] for i in range(UpperCamelCase__ )]
							snake_case_     							=       [
							    [a[i][j] for j in range(UpperCamelCase__  ,				UpperCamelCase__ )] for i in range(UpperCamelCase__  ,				UpperCamelCase__ )
							]

							snake_case_     							=       [[a[i][j] for j in range(UpperCamelCase__ )] for i in range(UpperCamelCase__ )]
							snake_case_     							=       [[a[i][j] for j in range(UpperCamelCase__ )] for i in range(UpperCamelCase__  ,				UpperCamelCase__ )]

							return top_left, top_right, bot_left, bot_right





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''simple docstring'''






							return len(UpperCamelCase__ ), len(matrix[0] )





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''simple docstring'''






							print('\n'.join(str(UpperCamelCase__ ) for line in matrix ) )





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							if matrix_dimensions(UpperCamelCase__ ) == (2, 2):
														return default_matrix_multiplication(UpperCamelCase__  ,				UpperCamelCase__ )

							snake_case_							,       snake_case_							,       snake_case_							,       snake_case_     							=       split_matrix(UpperCamelCase__ )
							snake_case_							,       snake_case_							,       snake_case_							,       snake_case_     							=       split_matrix(UpperCamelCase__ )

							snake_case_     							=       actual_strassen(UpperCamelCase__  ,				matrix_subtraction(UpperCamelCase__  ,				UpperCamelCase__ ) )
							snake_case_     							=       actual_strassen(matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )  ,				UpperCamelCase__ )
							snake_case_     							=       actual_strassen(matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )  ,				UpperCamelCase__ )
							snake_case_     							=       actual_strassen(UpperCamelCase__  ,				matrix_subtraction(UpperCamelCase__  ,				UpperCamelCase__ ) )
							snake_case_     							=       actual_strassen(matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )  ,				matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ ) )
							snake_case_     							=       actual_strassen(matrix_subtraction(UpperCamelCase__  ,				UpperCamelCase__ )  ,				matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ ) )
							snake_case_     							=       actual_strassen(matrix_subtraction(UpperCamelCase__  ,				UpperCamelCase__ )  ,				matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ ) )

							snake_case_     							=       matrix_addition(matrix_subtraction(matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )  ,				UpperCamelCase__ )  ,				UpperCamelCase__ )
							snake_case_     							=       matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )
							snake_case_     							=       matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )
							snake_case_     							=       matrix_subtraction(matrix_subtraction(matrix_addition(UpperCamelCase__  ,				UpperCamelCase__ )  ,				UpperCamelCase__ )  ,				UpperCamelCase__ )

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





def    __lowerCamelCase      (					UpperCamelCase__  ,				UpperCamelCase__ ):







							'''simple docstring'''






							if matrix_dimensions(UpperCamelCase__ )[1] != matrix_dimensions(UpperCamelCase__ )[0]:
														snake_case_     							=       (
														    'Unable to multiply these matrices, please check the dimensions.\n'
														    F'''Matrix A: {matrixa}\n'''
														    F'''Matrix B: {matrixa}'''
														)
														raise Exception(UpperCamelCase__ )
							snake_case_     							=       matrix_dimensions(UpperCamelCase__ )
							snake_case_     							=       matrix_dimensions(UpperCamelCase__ )

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

							snake_case_     							=       max(*UpperCamelCase__  ,				*UpperCamelCase__ )
							snake_case_     							=       int(math.pow(2  ,				math.ceil(math.loga(UpperCamelCase__ ) ) ) )
							snake_case_     							=       matrixa
							snake_case_     							=       matrixa

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

							snake_case_     							=       actual_strassen(UpperCamelCase__  ,				UpperCamelCase__ )

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


if __name__ == "__main__":
					_UpperCAmelCase						:  Dict									=			[
					    [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],
					]
					_UpperCAmelCase						:  Optional[Any]									=			[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
					print(strassen(matrixa, matrixa))







_UpperCAmelCase						:  Any									=			6_5521





def    __lowerCamelCase      (					UpperCamelCase__ ):







							'''simple docstring'''






							snake_case_     							=       1
							snake_case_     							=       0
							for plain_chr in plain_text:
														snake_case_     							=       (a + ord(UpperCamelCase__ )) % MOD_ADLER
														snake_case_     							=       (b + a) % MOD_ADLER
							return (b << 16) | a




