






def 						_a    (      a :int	,							a :bool = False )							->			bool:
 if n == 2:
  return True
 if not n % 2 or n < 2:
  return False
 if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
  return False
 if n > 3_317_044_064_679_887_385_961_981 and not allow_probable:
  raise ValueError(
      '''Warning: upper bound of deterministic test is exceeded. '''
      '''Pass allow_probable=True to allow probabilistic test. '''
      '''A return value of True indicates a probable prime.''' )
 # array bounds provided by analysis
 a		  =      [
     2_047,
     1_373_653,
     25_326_001,
     3_215_031_751,
     2_152_302_898_747,
     3_474_749_660_383,
     341_550_071_728_321,
     1,
     3_825_123_056_546_413_051,
     1,
     1,
     318_665_857_834_031_151_167_461,
     3_317_044_064_679_887_385_961_981,
 ]

 a		  =      [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
 for idx, _p in enumerate(a	,							1 ):
  if n < _p:
   # then we have our last prime to check
   a		  =      primes[:idx]
   break
 a  ,     a		  =      n - 1, 0
 # break up n -1 into a power of 2 (s) and
 # remaining odd component
 # essentially, solve for d * 2 ** s == n - 1
 while d % 2 == 0:
  d //= 2
  s += 1
 for prime in plist:
  a		  =      False
  for r in range(a ):
   a		  =      pow(a	,							d * 2**r	,							a )
   # see article for analysis explanation for m
   if (r == 0 and m == 1) or ((m + 1) % n == 0):
    a		  =      True
    # this loop will not determine compositeness
    break
  if pr:
   continue
  # if pr is False, then the above loop never evaluated to true,
  # and the n MUST be composite
  return False
 return True
def 						_a    (      )							->			None:
 assert not miller_rabin(561 )
 assert miller_rabin(563 )
 # 2047

 assert not miller_rabin(838_201 )
 assert miller_rabin(838_207 )
 # 1_373_653

 assert not miller_rabin(17_316_001 )
 assert miller_rabin(17_316_017 )
 # 25_326_001

 assert not miller_rabin(3_078_386_641 )
 assert miller_rabin(3_078_386_653 )
 # 3_215_031_751

 assert not miller_rabin(1_713_045_574_801 )
 assert miller_rabin(1_713_045_574_819 )
 # 2_152_302_898_747

 assert not miller_rabin(2_779_799_728_307 )
 assert miller_rabin(2_779_799_728_327 )
 # 3_474_749_660_383

 assert not miller_rabin(113_850_023_909_441 )
 assert miller_rabin(113_850_023_909_527 )
 # 341_550_071_728_321

 assert not miller_rabin(1_275_041_018_848_804_351 )
 assert miller_rabin(1_275_041_018_848_804_391 )
 # 3_825_123_056_546_413_051

 assert not miller_rabin(79_666_464_458_507_787_791_867 )
 assert miller_rabin(79_666_464_458_507_787_791_951 )
 # 318_665_857_834_031_151_167_461

 assert not miller_rabin(552_840_677_446_647_897_660_333 )
 assert miller_rabin(552_840_677_446_647_897_660_359 )
 # 3_317_044_064_679_887_385_961_981
 # upper limit for probabilistic test


if __name__ == "__main__":
     test_miller_rabin()







from pathlib import Path

import fire


def 			UpperCamelCase(  __UpperCamelCase							:		str     ,__UpperCamelCase							:		str     ,__UpperCamelCase							:		int ):
		lowerCAmelCase_			:     List[str]									= Path(__UpperCamelCase )
		lowerCAmelCase_			:     Union[str, Any]									= Path(__UpperCamelCase )
		dest_dir.mkdir(exist_ok=__UpperCamelCase )
		for path in src_dir.iterdir():
				lowerCAmelCase_			:     Optional[Any]									= [x.rstrip() for x in list(path.open().readlines() )][:n]
				lowerCAmelCase_			:     List[str]									= dest_dir.joinpath(path.name )
				print(__UpperCamelCase )
				dest_path.open('''w''' ).write('''\n'''.join(__UpperCamelCase ) )


if __name__ == "__main__":
						fire.Fire(minify)





