





from collections import defaultdict
from math import gcd






def lowerCamelCase__    (							snake_case_	:  int = 150_0000       )      ->				int:
   __snake_case							       =   defaultdict(snake_case_       )
   __snake_case							       =   2
   while 2 * euclid_m * (euclid_m + 1) <= limit:
      for euclid_n in range((euclid_m % 2) + 1       ,      snake_case_       ,      2       ):
         if gcd(snake_case_       ,      snake_case_       ) > 1:
            continue
         __snake_case							       =   2 * euclid_m * (euclid_m + euclid_n)
         for perimeter in range(snake_case_       ,      limit + 1       ,      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() = }')








from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       )      ->				list[list[int]]:
   __snake_case							       =   []
   __snake_case							       =   []
   __snake_case							       =   0
   __snake_case							       =   sum(snake_case_       )
   create_state_space_tree(snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       )
   return result






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       ,      snake_case_	:  int       ,      snake_case_	:  list[int]       ,      snake_case_	:  list[list[int]]       ,      snake_case_	:  int       ,      )      ->				None:
   if sum(snake_case_       ) > max_sum or (remaining_nums_sum + sum(snake_case_       )) < max_sum:
      return
   if sum(snake_case_       ) == max_sum:
      result.append(snake_case_       )
      return
   for index in range(snake_case_       ,      len(snake_case_       )       ):
      create_state_space_tree(
          snake_case_       ,      snake_case_       ,      index + 1       ,      [*path, nums[index]]       ,      snake_case_       ,      remaining_nums_sum - nums[index]       ,      )
snake_case_				=			[3, 34, 4, 12, 5, 2]
snake_case_				=			9
snake_case_				=			generate_sum_of_subsets_soln(nums, max_sum)







print(*result)

