




"""simple docstring"""





from __future__ import annotations

import math

def        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      list:


			"""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"				)
			__UpperCAmelCase						:			Optional[Any]												=       [
			    [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        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      Dict:


			"""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        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      Optional[Any]:


			"""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        _UpperCamelCase     (      UpperCamelCase				)      ->      tuple[list, list, list, list]:


			"""simple docstring"""
			if len(UpperCamelCase				) % 2 != 0 or len(a[0]				) % 2 != 0:
						raise Exception("Odd matrices are not supported!"				)

			__UpperCAmelCase						:			List[str]												=       len(UpperCamelCase				)
			__UpperCAmelCase						:			int												=       matrix_length // 2

			__UpperCAmelCase						:			Tuple												=       [[a[i][j] for j in range(UpperCamelCase					,							UpperCamelCase				)] for i in range(UpperCamelCase				)]
			__UpperCAmelCase						:			Dict												=       [
			    [a[i][j] for j in range(UpperCamelCase					,							UpperCamelCase				)] for i in range(UpperCamelCase					,							UpperCamelCase				)
			]

			__UpperCAmelCase						:			List[Any]												=       [[a[i][j] for j in range(UpperCamelCase				)] for i in range(UpperCamelCase				)]
			__UpperCAmelCase						:			Any												=       [[a[i][j] for j in range(UpperCamelCase				)] for i in range(UpperCamelCase					,							UpperCamelCase				)]

			return top_left, top_right, bot_left, bot_right

def        _UpperCamelCase     (      UpperCamelCase				)      ->      tuple[int, int]:


			"""simple docstring"""
			return len(UpperCamelCase				), len(matrix[0]				)

def        _UpperCamelCase     (      UpperCamelCase				)      ->      None:


			"""simple docstring"""
			print("\n".join(str(UpperCamelCase				) for line in matrix				)				)

def        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      list:


			"""simple docstring"""
			if matrix_dimensions(UpperCamelCase				) == (2, 2):
						return default_matrix_multiplication(UpperCamelCase					,							UpperCamelCase				)

			__UpperCAmelCase						,  __UpperCAmelCase						,  __UpperCAmelCase						,  __UpperCAmelCase						:			Union[str, Any]												=       split_matrix(UpperCamelCase				)
			__UpperCAmelCase						,  __UpperCAmelCase						,  __UpperCAmelCase						,  __UpperCAmelCase						:			Tuple												=       split_matrix(UpperCamelCase				)

			__UpperCAmelCase						:			Dict												=       actual_strassen(UpperCamelCase					,							matrix_subtraction(UpperCamelCase					,							UpperCamelCase				)				)
			__UpperCAmelCase						:			str												=       actual_strassen(matrix_addition(UpperCamelCase					,							UpperCamelCase				)					,							UpperCamelCase				)
			__UpperCAmelCase						:			Optional[Any]												=       actual_strassen(matrix_addition(UpperCamelCase					,							UpperCamelCase				)					,							UpperCamelCase				)
			__UpperCAmelCase						:			Optional[Any]												=       actual_strassen(UpperCamelCase					,							matrix_subtraction(UpperCamelCase					,							UpperCamelCase				)				)
			__UpperCAmelCase						:			Optional[Any]												=       actual_strassen(matrix_addition(UpperCamelCase					,							UpperCamelCase				)					,							matrix_addition(UpperCamelCase					,							UpperCamelCase				)				)
			__UpperCAmelCase						:			str												=       actual_strassen(matrix_subtraction(UpperCamelCase					,							UpperCamelCase				)					,							matrix_addition(UpperCamelCase					,							UpperCamelCase				)				)
			__UpperCAmelCase						:			Dict												=       actual_strassen(matrix_subtraction(UpperCamelCase					,							UpperCamelCase				)					,							matrix_addition(UpperCamelCase					,							UpperCamelCase				)				)

			__UpperCAmelCase						:			List[Any]												=       matrix_addition(matrix_subtraction(matrix_addition(UpperCamelCase					,							UpperCamelCase				)					,							UpperCamelCase				)					,							UpperCamelCase				)
			__UpperCAmelCase						:			Dict												=       matrix_addition(UpperCamelCase					,							UpperCamelCase				)
			__UpperCAmelCase						:			List[str]												=       matrix_addition(UpperCamelCase					,							UpperCamelCase				)
			__UpperCAmelCase						:			Any												=       matrix_subtraction(matrix_subtraction(matrix_addition(UpperCamelCase					,							UpperCamelCase				)					,							UpperCamelCase				)					,							UpperCamelCase				)

			# construct the new matrix from our 4 quadrants
			__UpperCAmelCase						:			str												=       []
			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        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      list:


			"""simple docstring"""
			if matrix_dimensions(UpperCamelCase				)[1] != matrix_dimensions(UpperCamelCase				)[0]:
						__UpperCAmelCase						:			List[str]												=       (
						    "Unable to multiply these matrices, please check the dimensions.\n"
						    f"Matrix A: {matrixa}\n"
						    f"Matrix B: {matrixa}"
						)
						raise Exception(UpperCamelCase				)
			__UpperCAmelCase						:			int												=       matrix_dimensions(UpperCamelCase				)
			__UpperCAmelCase						:			Any												=       matrix_dimensions(UpperCamelCase				)

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

			__UpperCAmelCase						:			Optional[int]												=       max(*UpperCamelCase					,							*UpperCamelCase				)
			__UpperCAmelCase						:			Optional[Any]												=       int(math.pow(2					,							math.ceil(math.loga(UpperCamelCase				)				)				)				)
			__UpperCAmelCase						:			List[str]												=       matrixa
			__UpperCAmelCase						:			Union[str, Any]												=       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				)

			__UpperCAmelCase						:			str												=       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__":
					A				=							[
					    [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],
					]
					A				=							[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
					print(strassen(matrixa, matrixa))




from __future__ import annotations



def 		UpperCamelCase     (       _UpperCAmelCase  :   str ,			_UpperCAmelCase  :   list[str] | None = None  )   ->			list[list[str]]:






						'''simple docstring'''

						_lowercase       :	Dict           =   word_bank or []
						# create a table
						_lowercase       :	int           =   len(_UpperCAmelCase  ) + 1

						_lowercase       :	list[list[list[str]]]           =   []
						for _ in range(_UpperCAmelCase  ):
												table.append([]  )
						# seed value
						_lowercase       :	Optional[int]           =   [[]]  # because empty string has empty combination

						# iterate through the indices
						for i in range(_UpperCAmelCase  ):
												# condition
												if table[i] != []:
																		for word in word_bank:
																								# slice condition
																								if target[i : i + len(_UpperCAmelCase  )] == word:
																														_lowercase       :	list[list[str]]           =   [
																														    [word, *way] for way in table[i]
																														]
																														# adds the word to every combination the current position holds
																														# now,push that combination to the table[i+len(word)]
																														table[i + len(_UpperCAmelCase  )] += new_combinations

    # combinations are in reverse order so reverse for better output
						for combination in table[len(_UpperCAmelCase  )]:
												combination.reverse()

						return table[len(_UpperCAmelCase  )]


if __name__ == "__main__":
							print(all_construct("""jwajalapa""", ["""jwa""", """j""", """w""", """a""", """la""", """lapa"""]))
							print(all_construct("""rajamati""", ["""s""", """raj""", """amat""", """raja""", """ma""", """i""", """t"""]))
							print(
							    all_construct(
							        """hexagonosaurus""",
							        ["""h""", """ex""", """hex""", """ag""", """ago""", """ru""", """auru""", """rus""", """go""", """no""", """o""", """s"""],
							    )
							)




