




'''simple docstring'''

from __future__ import annotations

import math


def 						__magic_name__       (      __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'''      )
					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 						__magic_name__       (      __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 						__magic_name__       (      __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 						__magic_name__       (      __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!'''      )

					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 						__magic_name__       (      __UpperCAmelCase      )						->   tuple[int, int]:

					'''simple docstring'''

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


def 						__magic_name__       (      __UpperCAmelCase      )						->   None:

					'''simple docstring'''

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


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   list:

					'''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 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   list:

					'''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__":
							a    :							Union[str, Any]										=    [
							    [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    :							Optional[int]										=    [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
							print(strassen(matrixa, matrixa))







'''simple docstring'''

import argparse
from collections import defaultdict

import yaml


a    :							List[Any]										=    'docs/source/en/_toctree.yml'


def 						__magic_name__       (      __UpperCAmelCase      )						->   str:

					'''simple docstring'''

					snake_case_		     =							defaultdict(__UpperCAmelCase      )
					for doc in model_doc:
										counts[doc["local"]] += 1
					snake_case_		     =							[key for key, value in counts.items() if value > 1]

					snake_case_		     =							[]
					for duplicate_key in duplicates:
										snake_case_		     =							list({doc['''title'''] for doc in model_doc if doc['''local'''] == duplicate_key}      )
										if len(__UpperCAmelCase      ) > 1:
															raise ValueError(
															    F"{duplicate_key} is present several times in the documentation table of content at "
															    '''`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the '''
															    '''others.'''      )
										# Only add this once
										new_doc.append({'''local''': duplicate_key, '''title''': titles[0]}      )

					# Add none duplicate-keys
					new_doc.extend([doc for doc in model_doc if counts[doc['''local''']] == 1]      )

					# Sort
					return sorted(__UpperCAmelCase, key=lambda __UpperCAmelCase      : s["title"].lower()      )


def 						__magic_name__       (      __UpperCAmelCase=False      )						->   List[Any]:

					'''simple docstring'''

					with open(__UpperCAmelCase, encoding='''utf-8'''      ) as f:
										snake_case_		     =							yaml.safe_load(f.read()      )

					# Get to the API doc
					snake_case_		     =							0
					while content[api_idx]["title"] != "API":
										api_idx += 1
					snake_case_		     =							content[api_idx]['''sections''']

					# Then to the model doc
					snake_case_		     =							0
					while api_doc[model_idx]["title"] != "Models":
										model_idx += 1

					snake_case_		     =							api_doc[model_idx]['''sections''']

					snake_case_		     =							[(idx, section) for idx, section in enumerate(__UpperCAmelCase      ) if '''sections''' in section]
					snake_case_		     =							False
					for idx, modality_doc in modalities_docs:
										snake_case_		     =							modality_doc['''sections''']
										snake_case_		     =							clean_model_doc_toc(__UpperCAmelCase      )

										if old_modality_doc != new_modality_doc:
															snake_case_		     =							True
															if overwrite:
																				snake_case_		     =							new_modality_doc

					if diff:
										if overwrite:
															snake_case_		     =							model_doc
															snake_case_		     =							api_doc
															with open(__UpperCAmelCase, '''w''', encoding='''utf-8'''      ) as f:
																				f.write(yaml.dump(__UpperCAmelCase, allow_unicode=__UpperCAmelCase      )      )
										else:
															raise ValueError(
															    '''The model doc part of the table of content is not properly sorted, run `make style` to fix this.'''      )


if __name__ == "__main__":
							a    :							Dict										=    argparse.ArgumentParser()
							parser.add_argument('--fix_and_overwrite', action='store_true', help='Whether to fix inconsistencies.')
							a    :							Union[str, Any]										=    parser.parse_args()

							check_model_doc(args.fix_and_overwrite)

