




from __future__ import annotations

import math







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			Optional[int]:



       """simple docstring"""

       if len(lowerCamelCase_		) != 2 or len(a[0]		) != 2 or len(lowerCamelCase_		) != 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 SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			Optional[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(lowerCamelCase_		)		)
       ]







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			str:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE							(			lowercase_		)  ->			Optional[Any]:



       """simple docstring"""

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

       A__ 					=       len(lowerCamelCase_		)
       A__ 					=       matrix_length // 2

       A__ 					=       [[a[i][j] for j in range(lowerCamelCase_					,							lowerCamelCase_		)] for i in range(lowerCamelCase_		)]
       A__ 					=       [
           [a[i][j] for j in range(lowerCamelCase_					,							lowerCamelCase_		)] for i in range(lowerCamelCase_					,							lowerCamelCase_		)
       ]

       A__ 					=       [[a[i][j] for j in range(lowerCamelCase_		)] for i in range(lowerCamelCase_		)]
       A__ 					=       [[a[i][j] for j in range(lowerCamelCase_		)] for i in range(lowerCamelCase_					,							lowerCamelCase_		)]

       return top_left, top_right, bot_left, bot_right







def SCREAMING_SNAKE_CASE							(			lowercase_		)  ->			Any:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE							(			lowercase_		)  ->			int:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			Dict:



       """simple docstring"""

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

       A__ 					=       split_matrix(lowerCamelCase_		)
       A__ 					=       split_matrix(lowerCamelCase_		)

       A__ 					=       actual_strassen(lowerCamelCase_					,							matrix_subtraction(lowerCamelCase_					,							lowerCamelCase_		)		)
       A__ 					=       actual_strassen(matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)					,							lowerCamelCase_		)
       A__ 					=       actual_strassen(matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)					,							lowerCamelCase_		)
       A__ 					=       actual_strassen(lowerCamelCase_					,							matrix_subtraction(lowerCamelCase_					,							lowerCamelCase_		)		)
       A__ 					=       actual_strassen(matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)					,							matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)		)
       A__ 					=       actual_strassen(matrix_subtraction(lowerCamelCase_					,							lowerCamelCase_		)					,							matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)		)
       A__ 					=       actual_strassen(matrix_subtraction(lowerCamelCase_					,							lowerCamelCase_		)					,							matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)		)

       A__ 					=       matrix_addition(matrix_subtraction(matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)					,							lowerCamelCase_		)					,							lowerCamelCase_		)
       A__ 					=       matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)
       A__ 					=       matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)
       A__ 					=       matrix_subtraction(matrix_subtraction(matrix_addition(lowerCamelCase_					,							lowerCamelCase_		)					,							lowerCamelCase_		)					,							lowerCamelCase_		)

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







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_		)  ->			Dict:



       """simple docstring"""

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

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

       A__ 					=       max(*lowerCamelCase_					,							*lowerCamelCase_		)
       A__ 					=       int(math.pow(2					,							math.ceil(math.loga(lowerCamelCase_		)		)		)		)
       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					,							lowerCamelCase_		):
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]					,							lowerCamelCase_		):
                            new_matrixa[i].append(0		)
              else:
                     new_matrixa.append([0] * maxim		)
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]					,							lowerCamelCase_		):
                            new_matrixa[i].append(0		)
              else:
                     new_matrixa.append([0] * maxim		)

       A__ 					=       actual_strassen(lowerCamelCase_					,							lowerCamelCase_		)

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


if __name__ == "__main__":
  _lowerCamelCase      :						List[str]							=  [
      [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],
  ]
  _lowerCamelCase      :						int							=  [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
  print(strassen(matrixa, matrixa))









'''simple docstring'''




from typing import TYPE_CHECKING

from ...file_utils import _LazyModule, is_tokenizers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


__UpperCAmelCase            =       {"""configuration_gpt_neox""": ["""GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoXConfig"""]}

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__UpperCAmelCase            =       ["""GPTNeoXTokenizerFast"""]

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__UpperCAmelCase            =       [
							    """GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """GPTNeoXForCausalLM""",
							    """GPTNeoXForQuestionAnswering""",
							    """GPTNeoXForSequenceClassification""",
							    """GPTNeoXForTokenClassification""",
							    """GPTNeoXLayer""",
							    """GPTNeoXModel""",
							    """GPTNeoXPreTrainedModel""",
							]


if TYPE_CHECKING:
							from .configuration_gpt_neox import GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoXConfig

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_gpt_neox_fast import GPTNeoXTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_gpt_neox import (
														    GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST,
														    GPTNeoXForCausalLM,
														    GPTNeoXForQuestionAnswering,
														    GPTNeoXForSequenceClassification,
														    GPTNeoXForTokenClassification,
														    GPTNeoXLayer,
														    GPTNeoXModel,
														    GPTNeoXPreTrainedModel,
														)


else:
							import sys

							__UpperCAmelCase            =       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



