

"""simple docstring"""
from __future__ import annotations

from typing import Any







def       UpperCamelCase_					(     *lowerCamelCase							:					list[list[int]]   )						->     list[list[int]]:



       """simple docstring"""







       if all(_check_not_integer(lowerCamelCase   ) for m in matrix_s   ):
              for i in matrix_s[1:]:
                     _verify_matrix_sizes(matrix_s[0]     , lowerCamelCase   )
              return [[sum(lowerCamelCase   ) for t in zip(*lowerCamelCase   )] for m in zip(*lowerCamelCase   )]
       raise TypeError('''Expected a matrix, got int/list instead'''   )







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]     , lowerCamelCase							:					list[list[int]]   )						->     list[list[int]]:



       """simple docstring"""







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







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]     , lowerCamelCase							:					int | float   )						->     list[list[float]]:



       """simple docstring"""







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







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]     , lowerCamelCase							:					list[list[int]]   )						->     list[list[int]]:



       """simple docstring"""







       if _check_not_integer(lowerCamelCase   ) and _check_not_integer(lowerCamelCase   ):
              __magic_name__       ,							__magic_name__			:		Union[str, Any]        =     _verify_matrix_sizes(lowerCamelCase     , lowerCamelCase   )

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







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     list[list[int]]:



       """simple docstring"""







       __magic_name__			:		Optional[int]        =     int(lowerCamelCase   )
       return [[int(row == column   ) for column in range(lowerCamelCase   )] for row in range(lowerCamelCase   )]







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]     , lowerCamelCase							:					bool = True   )						->     list[list[int]] | map[list[int]]:



       """simple docstring"""







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







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]     , lowerCamelCase							:					int     , lowerCamelCase							:					int   )						->     list[list[int]]:



       """simple docstring"""







       __magic_name__			:		Optional[int]        =     matrix[:row] + matrix[row + 1 :]
       return [row[:column] + row[column + 1 :] for row in minor]







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]   )						->     Any:



       """simple docstring"""







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

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







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]   )						->     list[list[float]] | None:



       """simple docstring"""







       __magic_name__			:		Optional[int]        =     determinant(lowerCamelCase   )
       if det == 0:
              return None

       __magic_name__			:		Optional[int]        =     [
           [determinant(minor(lowerCamelCase     , lowerCamelCase     , lowerCamelCase   )   ) for j in range(len(lowerCamelCase   )   )]
           for i in range(len(lowerCamelCase   )   )
       ]

       __magic_name__			:		Any        =     [
           [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]   )]
           for row in range(len(lowerCamelCase   )   )
       ]
       __magic_name__			:		Union[str, Any]        =     list(transpose(lowerCamelCase   )   )
       return scalar_multiply(lowerCamelCase     , 1 / det   )







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]   )						->     bool:



       """simple docstring"""







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







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]   )						->     tuple[int, int]:



       """simple docstring"""







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







def       UpperCamelCase_					(     lowerCamelCase							:					list[list[int]]     , lowerCamelCase							:					list[list[int]]   )						->     tuple[tuple[int, int], tuple[int, int]]:



       """simple docstring"""







       __magic_name__			:		List[Any]        =     _shape(lowerCamelCase   ) + _shape(lowerCamelCase   )
       if shape[0] != shape[3] or shape[1] != shape[2]:
              __magic_name__			:		Tuple        =     (
                  '''operands could not be broadcast together with shape '''
                  f"""({shape[0], shape[1]}), ({shape[2], shape[3]})"""
              )
              raise ValueError(lowerCamelCase   )
       return (shape[0], shape[2]), (shape[1], shape[3])







def       UpperCamelCase_					(     )						->     None:



       """simple docstring"""







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


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()



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

class        _UpperCamelCase	:


  """simple docstring"""





  snake_case_        =    'block_{0}.dat'



  def __init__( self					: int       ,       snake_case					: int      )	->			List[str]:


         '''simple docstring'''





         __magic_name__			:		Optional[int]        =     filename
         __magic_name__			:		Any        =     []



  def 							_UpperCAmelCase      ( self					: Optional[Any]       ,       snake_case					: int       ,       snake_case					: Any      )	->			List[Any]:


         '''simple docstring'''





         __magic_name__			:		Optional[Any]        =     self.BLOCK_FILENAME_FORMAT.format(snake_case      )
         with open(snake_case       ,       '''w'''      ) as file:
                file.write(snake_case      )
         self.block_filenames.append(snake_case      )



  def 							_UpperCAmelCase      ( self					: str      )	->			List[str]:


         '''simple docstring'''





         return self.block_filenames



  def 							_UpperCAmelCase      ( self					: Union[str, Any]       ,       snake_case					: Dict       ,       snake_case					: int=None      )	->			Union[str, Any]:


         '''simple docstring'''





         __magic_name__			:		List[str]        =     0
         with open(self.filename      ) as file:
                while True:
                       __magic_name__			:		Tuple        =     file.readlines(snake_case      )

                       if lines == []:
                              break

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

                       self.write_block(''''''.join(snake_case      )       ,       snake_case      )
                       i += 1




  def 							_UpperCAmelCase      ( self					: Tuple      )	->			Optional[int]:


         '''simple docstring'''





         map(os.remove       ,       self.block_filenames      )

class        _UpperCamelCase	:


  """simple docstring"""





  def 							_UpperCAmelCase      ( self					: List[Any]       ,       snake_case					: Dict      )	->			int:


         '''simple docstring'''





         __magic_name__			:		Any        =     -1
         __magic_name__			:		Union[str, Any]        =     None

         for i in range(len(snake_case      )      ):
                if min_str is None or choices[i] < min_str:
                       __magic_name__			:		Dict        =     i

         return min_index

class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: str       ,       snake_case					: Optional[int]      )	->			Any:


         '''simple docstring'''





         __magic_name__			:		Dict        =     files
         __magic_name__			:		List[str]        =     set()
         __magic_name__			:		Any        =     len(snake_case      )
         __magic_name__			:		int        =     {i: None for i in range(self.num_buffers      )}



  def 							_UpperCAmelCase      ( self					: List[str]      )	->			Optional[Any]:


         '''simple docstring'''





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



  def 							_UpperCAmelCase      ( self					: int      )	->			int:


         '''simple docstring'''





         for i in range(self.num_buffers      ):
                if self.buffers[i] is None and i not in self.empty:
                       __magic_name__			:		int        =     self.files[i].readline()

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

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

         return True




  def 							_UpperCAmelCase      ( self					: Dict       ,       snake_case					: Optional[Any]      )	->			Optional[Any]:


         '''simple docstring'''





         __magic_name__			:		List[str]        =     self.buffers[index]
         __magic_name__			:		Dict        =     None

         return value

class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: Any       ,       snake_case					: str      )	->			Dict:


         '''simple docstring'''





         __magic_name__			:		Optional[Any]        =     merge_strategy



  def 							_UpperCAmelCase      ( self					: Optional[int]       ,       snake_case					: int       ,       snake_case					: Dict       ,       snake_case					: Dict      )	->			Union[str, Any]:


         '''simple docstring'''





         __magic_name__			:		Union[str, Any]        =     FilesArray(self.get_file_handles(snake_case       ,       snake_case      )      )
         with open(snake_case       ,       '''w'''       ,       snake_case      ) as outfile:
                while buffers.refresh():
                       __magic_name__			:		List[str]        =     self.merge_strategy.select(buffers.get_dict()      )
                       outfile.write(buffers.unshift(snake_case      )      )




  def 							_UpperCAmelCase      ( self					: Union[str, Any]       ,       snake_case					: List[str]       ,       snake_case					: Optional[int]      )	->			Union[str, Any]:


         '''simple docstring'''





         __magic_name__			:		str        =     {}

         for i in range(len(snake_case      )      ):
                __magic_name__			:		Any        =     open(filenames[i]       ,       '''r'''       ,       snake_case      )  # noqa: UP015

         return files

class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: Optional[Any]       ,       snake_case					: Union[str, Any]      )	->			Optional[int]:


         '''simple docstring'''





         __magic_name__			:		int        =     block_size



  def 							_UpperCAmelCase      ( self					: str       ,       snake_case					: Optional[int]       ,       snake_case					: Dict=None      )	->			Optional[Any]:


         '''simple docstring'''





         __magic_name__			:		Tuple        =     self.get_number_blocks(snake_case       ,       self.block_size      )
         __magic_name__			:		str        =     FileSplitter(snake_case      )
         splitter.split(self.block_size       ,       snake_case      )

         __magic_name__			:		int        =     FileMerger(NWayMerge()      )
         __magic_name__			:		Any        =     self.block_size / (num_blocks + 1)
         merger.merge(splitter.get_block_filenames()       ,       filename + '''.out'''       ,       snake_case      )

         splitter.cleanup()




  def 							_UpperCAmelCase      ( self					: Tuple       ,       snake_case					: List[str]       ,       snake_case					: Union[str, Any]      )	->			Tuple:


         '''simple docstring'''





         return (os.stat(snake_case      ).st_size / block_size) + 1







def       UpperCamelCase_					(     lowerCamelCase							:					Union[str, Any]   )						->     Union[str, Any]:



       """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(lowerCamelCase   )







def       UpperCamelCase_					(     )						->     Optional[Any]:



       """simple docstring"""







       __magic_name__			:		Tuple        =     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'''   )
       __magic_name__			:		List[str]        =     parser.parse_args()

       __magic_name__			:		Any        =     ExternalSort(parse_memory(args.mem   )   )
       sorter.sort(args.filename[0]   )


if __name__ == "__main__":
 main()
