

def        __lowerCAmelCase    (       _UpperCamelCase		:  int		,							_UpperCamelCase		:  bool = False	)		->							bool:
 '''simple docstring'''


 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_31_70_44_06_46_79_88_73_85_96_19_81 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
 SCREAMING_SNAKE_CASE								=			[
     20_47,
     1_37_36_53,
     25_32_60_01,
     32_15_03_17_51,
     2_15_23_02_89_87_47,
     3_47_47_49_66_03_83,
     3_41_55_00_71_72_83_21,
     1,
     3_82_51_23_05_65_46_41_30_51,
     1,
     1,
     31_86_65_85_78_34_03_11_51_16_74_61,
     3_31_70_44_06_46_79_88_73_85_96_19_81,
 ]

 SCREAMING_SNAKE_CASE								=			[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
 for idx, _p in enumerate(_UpperCamelCase		,							1	):
  if n < _p:
   # then we have our last prime to check
   SCREAMING_SNAKE_CASE								=			primes[:idx]
   break
 SCREAMING_SNAKE_CASE						,	SCREAMING_SNAKE_CASE								=			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:
  SCREAMING_SNAKE_CASE								=			False
  for r in range(_UpperCamelCase	):
   SCREAMING_SNAKE_CASE								=			pow(_UpperCamelCase		,							d * 2**r		,							_UpperCamelCase	)
   # see article for analysis explanation for m
   if (r == 0 and m == 1) or ((m + 1) % n == 0):
    SCREAMING_SNAKE_CASE								=			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        __lowerCAmelCase    (       )		->							None:
 '''simple docstring'''


 assert not miller_rabin(5_61	)
 assert miller_rabin(5_63	)
 # 2047

 assert not miller_rabin(83_82_01	)
 assert miller_rabin(83_82_07	)
 # 1_373_653

 assert not miller_rabin(17_31_60_01	)
 assert miller_rabin(17_31_60_17	)
 # 25_326_001

 assert not miller_rabin(30_78_38_66_41	)
 assert miller_rabin(30_78_38_66_53	)
 # 3_215_031_751

 assert not miller_rabin(1_71_30_45_57_48_01	)
 assert miller_rabin(1_71_30_45_57_48_19	)
 # 2_152_302_898_747

 assert not miller_rabin(2_77_97_99_72_83_07	)
 assert miller_rabin(2_77_97_99_72_83_27	)
 # 3_474_749_660_383

 assert not miller_rabin(1_13_85_00_23_90_94_41	)
 assert miller_rabin(1_13_85_00_23_90_95_27	)
 # 341_550_071_728_321

 assert not miller_rabin(1_27_50_41_01_88_48_80_43_51	)
 assert miller_rabin(1_27_50_41_01_88_48_80_43_91	)
 # 3_825_123_056_546_413_051

 assert not miller_rabin(7_96_66_46_44_58_50_77_87_79_18_67	)
 assert miller_rabin(7_96_66_46_44_58_50_77_87_79_19_51	)
 # 318_665_857_834_031_151_167_461

 assert not miller_rabin(55_28_40_67_74_46_64_78_97_66_03_33	)
 assert miller_rabin(55_28_40_67_74_46_64_78_97_66_03_59	)
 # 3_317_044_064_679_887_385_961_981
 # upper limit for probabilistic test


if __name__ == "__main__":
      test_miller_rabin()




def        __lowerCAmelCase    (       _UpperCamelCase		:  int = 10_00	)		->							int:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE								=			2**power
 SCREAMING_SNAKE_CASE								=			str(_UpperCamelCase	)
 SCREAMING_SNAKE_CASE								=			list(_UpperCamelCase	)
 SCREAMING_SNAKE_CASE								=			0

 for i in list_num:
  sum_of_num += int(_UpperCamelCase	)

 return sum_of_num


if __name__ == "__main__":
      a_    :						List[str]    		=      int(input("Enter the power of 2: ").strip())
      print("2 ^ ", power, " = ", 2**power)
      a_    :						int    		=      solution(power)
      print("Sum of the digits is: ", result)

