




'''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	)		->					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	)		->					int:

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



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_speech_available,
    is_torch_available,
)


__a  			=					{
    'configuration_trocr': ['TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP', 'TrOCRConfig'],
    'processing_trocr': ['TrOCRProcessor'],
}


try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a  			=					[
						    'TROCR_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'TrOCRForCausalLM',
						    'TrOCRPreTrainedModel',
						]


if TYPE_CHECKING:
						from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
						from .processing_trocr import TrOCRProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
						import sys

						__a  			=					_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




