





from collections import defaultdict
from math import gcd
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 1_50_00_00						)  ->  int:






   """simple docstring"""







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


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







'''simple docstring'''



from __future__ import annotations


def 				lowercase_					(     __A			:							list[list[int]]      )							->   int:



 """simple docstring"""




 for i in range(1       ,   len(matrix[0]      )      ):
  matrix[0][i] += matrix[0][i - 1]

 # preprocessing the first column
 for i in range(1       ,   len(__A      )      ):
  matrix[i][0] += matrix[i - 1][0]

 # updating the path cost for current position
 for i in range(1       ,   len(__A      )      ):
  for j in range(1       ,   len(matrix[0]      )      ):
   matrix[i][j] += min(matrix[i - 1][j]       ,   matrix[i][j - 1]      )

 return matrix[-1][-1]


if __name__ == "__main__":
      import doctest

      doctest.testmod()



