



from __future__ import annotations

from typing import Any

def 					lowerCAmelCase__  (							*_SCREAMING_SNAKE_CASE    :     Union[str, Any]      ):
				"""simple docstring"""







				if all(_check_not_integer(_A      ) for m in matrix_s      ):
								for i in matrix_s[1:]:
												_verify_matrix_sizes(matrix_s[0]			,       _A      )
								return [[sum(_A      ) for t in zip(*_A      )] for m in zip(*_A      )]
				raise TypeError("""Expected a matrix, got int/list instead"""      )

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     int			,       _SCREAMING_SNAKE_CASE    :     Dict      ):
				"""simple docstring"""







				if (
				    _check_not_integer(_A      )
				    and _check_not_integer(_A      )
				    and _verify_matrix_sizes(_A			,       _A      )
				):
								return [[i - j for i, j in zip(*_A      )] for m in zip(_A			,       _A      )]
				raise TypeError("""Expected a matrix, got int/list instead"""      )

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Union[str, Any]			,       _SCREAMING_SNAKE_CASE    :     Union[str, Any]      ):
				"""simple docstring"""







				return [[x * n for x in row] for row in matrix]

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Dict			,       _SCREAMING_SNAKE_CASE    :     List[Any]      ):
				"""simple docstring"""







				if _check_not_integer(_A      ) and _check_not_integer(_A      ):
								__a       ,   __a					       =						_verify_matrix_sizes(_A			,       _A      )

				if cols[0] != rows[1]:
								__a					       =						(
								    """Cannot multiply matrix of dimensions """
								    f"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
								)
								raise ValueError(_A      )
				return [
				    [sum(m * n for m, n in zip(_A			,       _A      )      ) for j in zip(*_A      )] for i in matrix_a
				]

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Any      ):
				"""simple docstring"""







				__a					       =						int(_A      )
				return [[int(row == column      ) for column in range(_A      )] for row in range(_A      )]

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Tuple			,       _SCREAMING_SNAKE_CASE    :     Dict = True      ):
				"""simple docstring"""







				if _check_not_integer(_A      ):
								if return_map:
												return map(_A			,       zip(*_A      )      )
								else:
												return list(map(_A			,       zip(*_A      )      )      )
				raise TypeError("""Expected a matrix, got int/list instead"""      )

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     int			,       _SCREAMING_SNAKE_CASE    :     Any			,       _SCREAMING_SNAKE_CASE    :     List[str]      ):
				"""simple docstring"""







				__a					       =						matrix[:row] + matrix[row + 1 :]
				return [row[:column] + row[column + 1 :] for row in minor]

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Optional[int]      ):
				"""simple docstring"""







				if len(_A      ) == 1:
								return matrix[0][0]

				return sum(
				    x * determinant(minor(_A			,       0			,       _A      )      ) * (-1) ** i
				    for i, x in enumerate(matrix[0]      )      )

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Optional[Any]      ):
				"""simple docstring"""







				__a					       =						determinant(_A      )
				if det == 0:
								return None

				__a					       =						[
				    [determinant(minor(_A			,       _A			,       _A      )      ) for j in range(len(_A      )      )]
				    for i in range(len(_A      )      )
				]

				__a					       =						[
				    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]      )]
				    for row in range(len(_A      )      )
				]
				__a					       =						list(transpose(_A      )      )
				return scalar_multiply(_A			,       1 / det      )

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     List[str]      ):
				"""simple docstring"""







				return not isinstance(_A			,       _A      ) and not isinstance(matrix[0]			,       _A      )

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     List[Any]      ):
				"""simple docstring"""







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

def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Dict			,       _SCREAMING_SNAKE_CASE    :     Optional[Any]      ):
				"""simple docstring"""







				__a					       =						_shape(_A      ) + _shape(_A      )
				if shape[0] != shape[3] or shape[1] != shape[2]:
								__a					       =						(
								    """operands could not be broadcast together with shape """
								    f"({shape[0], shape[1]}), ({shape[2], shape[3]})"
								)
								raise ValueError(_A      )
				return (shape[0], shape[2]), (shape[1], shape[3])

def 					lowerCAmelCase__  (							):
				"""simple docstring"""







				__a					       =						[[12, 10], [3, 9]]
				__a					       =						[[3, 4], [7, 4]]
				__a					       =						[[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
				__a					       =						[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
				print(f"Add Operation, {add(_A			,       _A      ) = } \n"      )
				print(
				    f"Multiply Operation, {multiply(_A			,       _A      ) = } \n"			,       )
				print(f"Identity: {identity(5      )}\n"      )
				print(f"Minor of {matrix_c} = {minor(_A			,       1			,       2      )} \n"      )
				print(f"Determinant of {matrix_b} = {determinant(_A      )} \n"      )
				print(f"Inverse of {matrix_d} = {inverse(_A      )}\n"      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()





#
# Sort large text files in a minimum amount of memory
#
import argparse
import os






class 				SCREAMING_SNAKE_CASE     :
							__lowerCamelCase		:		Tuple      ='block_{0}.dat'





							def __init__(				self						:						int ,			__lowercase						:						Dict		):

											'''simple docstring'''
											__a					       =						filename
											__a					       =						[]





							def   UpperCamelCase_   (				self						:						int ,			__lowercase						:						Dict ,			__lowercase						:						Optional[Any]		):

											'''simple docstring'''
											__a					       =						self.BLOCK_FILENAME_FORMAT.format(__lowercase		)
											with open(__lowercase ,			"""w"""		) as file:
															file.write(__lowercase		)
											self.block_filenames.append(__lowercase		)





							def   UpperCamelCase_   (				self						:						List[str]		):

											'''simple docstring'''
											return self.block_filenames





							def   UpperCamelCase_   (				self						:						Any ,			__lowercase						:						str ,			__lowercase						:						Tuple=None		):

											'''simple docstring'''
											__a					       =						0
											with open(self.filename		) as file:
															while True:
																			__a					       =						file.readlines(__lowercase		)

																			if lines == []:
																							break

																			if sort_key is None:
																							lines.sort()
																			else:
																							lines.sort(key=__lowercase		)

																			self.write_block("""""".join(__lowercase		) ,			__lowercase		)
																			i += 1







							def   UpperCamelCase_   (				self						:						List[Any]		):

											'''simple docstring'''
											map(os.remove ,			self.block_filenames		)






class 				SCREAMING_SNAKE_CASE     :





							def   UpperCamelCase_   (				self						:						Dict ,			__lowercase						:						Optional[Any]		):

											'''simple docstring'''
											__a					       =						-1
											__a					       =						None

											for i in range(len(__lowercase		)		):
															if min_str is None or choices[i] < min_str:
																			__a					       =						i

											return min_index






class 				SCREAMING_SNAKE_CASE     :





							def __init__(				self						:						Optional[int] ,			__lowercase						:						Optional[Any]		):

											'''simple docstring'''
											__a					       =						files
											__a					       =						set()
											__a					       =						len(__lowercase		)
											__a					       =						{i: None for i in range(self.num_buffers		)}





							def   UpperCamelCase_   (				self						:						int		):

											'''simple docstring'''
											return {
											    i: self.buffers[i] for i in range(self.num_buffers		) if i not in self.empty
											}





							def   UpperCamelCase_   (				self						:						List[str]		):

											'''simple docstring'''
											for i in range(self.num_buffers		):
															if self.buffers[i] is None and i not in self.empty:
																			__a					       =						self.files[i].readline()

																			if self.buffers[i] == "":
																							self.empty.add(__lowercase		)
																							self.files[i].close()

											if len(self.empty		) == self.num_buffers:
															return False

											return True







							def   UpperCamelCase_   (				self						:						List[str] ,			__lowercase						:						List[Any]		):

											'''simple docstring'''
											__a					       =						self.buffers[index]
											__a					       =						None

											return value






class 				SCREAMING_SNAKE_CASE     :





							def __init__(				self						:						Optional[int] ,			__lowercase						:						Any		):

											'''simple docstring'''
											__a					       =						merge_strategy





							def   UpperCamelCase_   (				self						:						str ,			__lowercase						:						Union[str, Any] ,			__lowercase						:						List[str] ,			__lowercase						:						Dict		):

											'''simple docstring'''
											__a					       =						FilesArray(self.get_file_handles(__lowercase ,			__lowercase		)		)
											with open(__lowercase ,			"""w""" ,			__lowercase		) as outfile:
															while buffers.refresh():
																			__a					       =						self.merge_strategy.select(buffers.get_dict()		)
																			outfile.write(buffers.unshift(__lowercase		)		)







							def   UpperCamelCase_   (				self						:						List[Any] ,			__lowercase						:						str ,			__lowercase						:						Dict		):

											'''simple docstring'''
											__a					       =						{}

											for i in range(len(__lowercase		)		):
															__a					       =						open(filenames[i] ,			"""r""" ,			__lowercase		)  # noqa: UP015

											return files






class 				SCREAMING_SNAKE_CASE     :





							def __init__(				self						:						str ,			__lowercase						:						Tuple		):

											'''simple docstring'''
											__a					       =						block_size





							def   UpperCamelCase_   (				self						:						Tuple ,			__lowercase						:						str ,			__lowercase						:						Union[str, Any]=None		):

											'''simple docstring'''
											__a					       =						self.get_number_blocks(__lowercase ,			self.block_size		)
											__a					       =						FileSplitter(__lowercase		)
											splitter.split(self.block_size ,			__lowercase		)

											__a					       =						FileMerger(NWayMerge()		)
											__a					       =						self.block_size / (num_blocks + 1)
											merger.merge(splitter.get_block_filenames() ,			filename + """.out""" ,			__lowercase		)

											splitter.cleanup()







							def   UpperCamelCase_   (				self						:						str ,			__lowercase						:						Optional[Any] ,			__lowercase						:						Dict		):

											'''simple docstring'''
											return (os.stat(__lowercase		).st_size / block_size) + 1



def 					lowerCAmelCase__  (							_SCREAMING_SNAKE_CASE    :     Tuple      ):
				"""simple docstring"""







				if string[-1].lower() == "k":
								return int(string[:-1]      ) * 1024
				elif string[-1].lower() == "m":
								return int(string[:-1]      ) * 1024 * 1024
				elif string[-1].lower() == "g":
								return int(string[:-1]      ) * 1024 * 1024 * 1024
				else:
								return int(_SCREAMING_SNAKE_CASE      )

def 					lowerCAmelCase__  (							):
				"""simple docstring"""







				__a					       =						argparse.ArgumentParser()
				parser.add_argument(
				    """-m"""			,       """--mem"""			,       help="""amount of memory to use for sorting"""			,       default="""100M"""      )
				parser.add_argument(
				    """filename"""			,       metavar="""<filename>"""			,       nargs=1			,       help="""name of file to sort"""      )
				__a					       =						parser.parse_args()

				__a					       =						ExternalSort(parse_memory(args.mem      )      )
				sorter.sort(args.filename[0]      )


if __name__ == "__main__":
						main()
