

"""simple docstring"""



from itertools import compress, repeat
from math import ceil, sqrt





def 			_snake_case  (     UpperCAmelCase_	:       int      ):

     if num <= 2:
          return []
     if num == 3:
          return [2]

     # Odd sieve for numbers in range [3, num - 1]
     A__				      =	bytearray(b"""\x01"""      ) * ((num >> 1) - 1)

     for i in range(3       , int(sqrt(UpperCAmelCase_      )      ) + 1       , 2      ):
          if sieve[(i >> 1) - 1]:
               A__				      =	i**2
               A__				      =	repeat(
                   0       , ceil((num - i_squared) / (i << 1)      )      )

     return [2] + list(compress(range(3       , UpperCAmelCase_       , 2      )       , UpperCAmelCase_      )      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()









"""simple docstring"""



from __future__ import annotations





def 			_snake_case  (     UpperCAmelCase_	:       list[list[int]]       , UpperCAmelCase_	:       list[list[int]]      ):
     assert len(UpperCAmelCase_      ) == len(UpperCAmelCase_      )

     A__				      =	len(UpperCAmelCase_      )
     A__				      =	list(range(UpperCAmelCase_      )      )
     A__				      =	[-1] * n  # who the donor has donated to
     A__				      =	[-1] * n  # who the recipient has received from
     A__				      =	[0] * n

     while unmatched_donors:
          A__				      =	unmatched_donors[0]
          A__				      =	donor_pref[donor]
          A__				      =	donor_preference[num_donations[donor]]
          num_donations[donor] += 1
          A__				      =	recipient_pref[recipient]
          A__				      =	rec_record[recipient]

          if prev_donor != -1:
               if rec_preference.index(UpperCAmelCase_      ) > rec_preference.index(UpperCAmelCase_      ):
                    A__				      =	donor
                    A__				      =	recipient
                    unmatched_donors.append(UpperCAmelCase_      )
                    unmatched_donors.remove(UpperCAmelCase_      )
          else:
               A__				      =	donor
               A__				      =	recipient
               unmatched_donors.remove(UpperCAmelCase_      )
     return donor_record






