from collections import defaultdict
from math import gcd




def    lowerCAmelCase_ (     __A = 1_500_000							)     ->				int:







      '''simple docstring'''


      UpperCAmelCase__								=  defaultdict(__A							)
      UpperCAmelCase__								=  2
      while 2 * euclid_m * (euclid_m + 1) <= limit:
            for euclid_n in range((euclid_m % 2) + 1,  __A,  2							):
                  if gcd(__A,  __A							) > 1:
                        continue
                  UpperCAmelCase__								=  2 * euclid_m * (euclid_m + euclid_n)
                  for perimeter in range(__A,  limit + 1,  __A							):
                        frequencies[perimeter] += 1
            euclid_m += 1
      return sum(1 for frequency in frequencies.values() if frequency == 1							)


if __name__ == "__main__":
      print(f'''{solution() = }''')




def    lowerCAmelCase_ (     __A,  __A							)     ->				float:







      '''simple docstring'''


      def get_matched_characters(__A,  __A							) -> str:
            UpperCAmelCase__								=  []
            UpperCAmelCase__								=  min(len(_stra							),  len(_stra							)							) // 2
            for i, l in enumerate(_stra							):
                  UpperCAmelCase__								=  int(max(0,  i - limit							)							)
                  UpperCAmelCase__								=  int(min(i + limit + 1,  len(_stra							)							)							)
                  if l in _stra[left:right]:
                        matched.append(__A							)
                        UpperCAmelCase__								=  f"""{_stra[0:_stra.index(__A							)]} {_stra[_stra.index(__A							) + 1:]}"""

            return "".join(__A							)

      # matching characters
      UpperCAmelCase__								=  get_matched_characters(__A,  __A							)
      UpperCAmelCase__								=  get_matched_characters(__A,  __A							)
      UpperCAmelCase__								=  len(__A							)

      # transposition
      UpperCAmelCase__								=  (
          len([(ca, ca) for ca, ca in zip(__A,  __A							) if ca != ca]							) // 2
      )

      if not match_count:
            UpperCAmelCase__								=  0.0
      else:
            UpperCAmelCase__								=  (
                1
                / 3
                * (
                    match_count / len(__A							)
                    + match_count / len(__A							)
                    + (match_count - transpositions) / match_count
                )
            )

      # common prefix up to 4 characters
      UpperCAmelCase__								=  0
      for ca, ca in zip(stra[:4],  stra[:4]							):
            if ca == ca:
                  prefix_len += 1
            else:
                  break

      return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      print(jaro_winkler('hello', 'world'))



