
'''simple docstring'''



def 				lowerCAmelCase_		(			SCREAMING_SNAKE_CASE_      , SCREAMING_SNAKE_CASE_  )       ->       list[list[int]]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE       	=			[]
   _SCREAMING_SNAKE_CASE       	=			len(SCREAMING_SNAKE_CASE_  )
   for i in range(SCREAMING_SNAKE_CASE_  ):
      _SCREAMING_SNAKE_CASE       	=			[]
      for j in range(SCREAMING_SNAKE_CASE_  ):
         _SCREAMING_SNAKE_CASE       	=			0
         for k in range(SCREAMING_SNAKE_CASE_  ):
            _SCREAMING_SNAKE_CASE       	=			val + matrix_a[i][k] * matrix_b[k][j]
         list_a.append(SCREAMING_SNAKE_CASE_  )
      matrix_c.append(SCREAMING_SNAKE_CASE_  )
   return matrix_c
def 				lowerCAmelCase_		(			SCREAMING_SNAKE_CASE_  )       ->       list[list[int]]:




   """simple docstring"""
   return [[int(row == column  ) for column in range(SCREAMING_SNAKE_CASE_  )] for row in range(SCREAMING_SNAKE_CASE_  )]
def 				lowerCAmelCase_		(			SCREAMING_SNAKE_CASE_  )       ->       int:




   """simple docstring"""
   if n <= 1:
      return n
   _SCREAMING_SNAKE_CASE       	=			identity(2  )
   _SCREAMING_SNAKE_CASE       	=			[[1, 1], [1, 0]]
   _SCREAMING_SNAKE_CASE       	=			n - 1
   while n > 0:
      if n % 2 == 1:
         _SCREAMING_SNAKE_CASE       	=			multiply(SCREAMING_SNAKE_CASE_      , SCREAMING_SNAKE_CASE_  )
      _SCREAMING_SNAKE_CASE       	=			multiply(SCREAMING_SNAKE_CASE_      , SCREAMING_SNAKE_CASE_  )
      _SCREAMING_SNAKE_CASE       	=			int(n / 2  )
   return res_matrix[0][0]
def 				lowerCAmelCase_		(			SCREAMING_SNAKE_CASE_  )       ->       int:




   """simple docstring"""
   if n <= 1:
      return n
   _SCREAMING_SNAKE_CASE       	=			0
   _SCREAMING_SNAKE_CASE       	=			1
   for _ in range(2      , n + 1  ):
      _SCREAMING_SNAKE_CASE	,							_SCREAMING_SNAKE_CASE       	=			fiba, fiba + fiba
   return fiba
def 				lowerCAmelCase_		(			)       ->       None:




   """simple docstring"""
   for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
      _SCREAMING_SNAKE_CASE       	=			int("""""".join(c for c in ordinal if c in """0123456789"""  )  )  # 1000th --> 1000
      print(
          F"{ordinal} fibonacci number using matrix exponentiation is "
          F"{nth_fibonacci_matrix(SCREAMING_SNAKE_CASE_  )} and using bruteforce is "
          F"{nth_fibonacci_bruteforce(SCREAMING_SNAKE_CASE_  )}\n"  )
   # from timeit import timeit
   # print(timeit("nth_fibonacci_matrix(1000000)",
   #              "from main import nth_fibonacci_matrix", number=5))
   # print(timeit("nth_fibonacci_bruteforce(1000000)",
   #              "from main import nth_fibonacci_bruteforce", number=5))
   # 2.3342058970001744
   # 57.256506615000035


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 				_a			:





       """simple docstring"""




       SCREAMING_SNAKE_CASE =					'block_{0}.dat'






       def __init__(							self    ,							A__ )      ->     Union[str, Any]:
          _SCREAMING_SNAKE_CASE       	=			filename
          _SCREAMING_SNAKE_CASE       	=			[]






       def     UpperCamelCase			(							self    ,							A__    ,							A__ )      ->     Optional[Any]:
          _SCREAMING_SNAKE_CASE       	=			self.BLOCK_FILENAME_FORMAT.format(A__ )
          with open(A__    ,							"""w""" ) as file:
             file.write(A__ )
          self.block_filenames.append(A__ )






       def     UpperCamelCase			(							self )      ->     Tuple:
          return self.block_filenames






       def     UpperCamelCase			(							self    ,							A__    ,							A__=None )      ->     Any:
          _SCREAMING_SNAKE_CASE       	=			0
          with open(self.filename ) as file:
             while True:
                _SCREAMING_SNAKE_CASE       	=			file.readlines(A__ )

                if lines == []:
                   break

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

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






       def     UpperCamelCase			(							self )      ->     List[Any]:
          map(os.remove    ,							self.block_filenames )






class 				_a			:





       """simple docstring"""




       def     UpperCamelCase			(							self    ,							A__ )      ->     str:
          _SCREAMING_SNAKE_CASE       	=			-1
          _SCREAMING_SNAKE_CASE       	=			None

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

          return min_index






class 				_a			:





       """simple docstring"""




       def __init__(							self    ,							A__ )      ->     Dict:
          _SCREAMING_SNAKE_CASE       	=			files
          _SCREAMING_SNAKE_CASE       	=			set()
          _SCREAMING_SNAKE_CASE       	=			len(A__ )
          _SCREAMING_SNAKE_CASE       	=			{i: None for i in range(self.num_buffers )}






       def     UpperCamelCase			(							self )      ->     Dict:
          return {
              i: self.buffers[i] for i in range(self.num_buffers ) if i not in self.empty
          }






       def     UpperCamelCase			(							self )      ->     Tuple:
          for i in range(self.num_buffers ):
             if self.buffers[i] is None and i not in self.empty:
                _SCREAMING_SNAKE_CASE       	=			self.files[i].readline()

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

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

          return True






       def     UpperCamelCase			(							self    ,							A__ )      ->     List[str]:
          _SCREAMING_SNAKE_CASE       	=			self.buffers[index]
          _SCREAMING_SNAKE_CASE       	=			None

          return value






class 				_a			:





       """simple docstring"""




       def __init__(							self    ,							A__ )      ->     str:
          _SCREAMING_SNAKE_CASE       	=			merge_strategy






       def     UpperCamelCase			(							self    ,							A__    ,							A__    ,							A__ )      ->     Union[str, Any]:
          _SCREAMING_SNAKE_CASE       	=			FilesArray(self.get_file_handles(A__    ,							A__ ) )
          with open(A__    ,							"""w"""    ,							A__ ) as outfile:
             while buffers.refresh():
                _SCREAMING_SNAKE_CASE       	=			self.merge_strategy.select(buffers.get_dict() )
                outfile.write(buffers.unshift(A__ ) )






       def     UpperCamelCase			(							self    ,							A__    ,							A__ )      ->     str:
          _SCREAMING_SNAKE_CASE       	=			{}

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

          return files






class 				_a			:





       """simple docstring"""




       def __init__(							self    ,							A__ )      ->     Union[str, Any]:
          _SCREAMING_SNAKE_CASE       	=			block_size






       def     UpperCamelCase			(							self    ,							A__    ,							A__=None )      ->     Optional[Any]:
          _SCREAMING_SNAKE_CASE       	=			self.get_number_blocks(A__    ,							self.block_size )
          _SCREAMING_SNAKE_CASE       	=			FileSplitter(A__ )
          splitter.split(self.block_size    ,							A__ )

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

          splitter.cleanup()






       def     UpperCamelCase			(							self    ,							A__    ,							A__ )      ->     Any:
          return (os.stat(A__ ).st_size / block_size) + 1






def 				lowerCAmelCase_		(			SCREAMING_SNAKE_CASE_  )       ->       str:




   """simple docstring"""
   if string[-1].lower() == "k":
      return int(string[:-1]  ) * 10_24
   elif string[-1].lower() == "m":
      return int(string[:-1]  ) * 10_24 * 10_24
   elif string[-1].lower() == "g":
      return int(string[:-1]  ) * 10_24 * 10_24 * 10_24
   else:
      return int(SCREAMING_SNAKE_CASE_  )
def 				lowerCAmelCase_		(			)       ->       List[str]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE       	=			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"""  )
   _SCREAMING_SNAKE_CASE       	=			parser.parse_args()

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


if __name__ == "__main__":
     main()






