


'''simple docstring'''

from __future__ import annotations

from collections.abc import Generator

def _SCREAMING_SNAKE_CASE ()			->			Generator[int, None, None]:






       """simple docstring"""







       lowercase__      =					{}
       lowercase__      =					2
       while True:
              lowercase__      =					factor_map.pop(A    ,					A			)
              if factor:
                     lowercase__      =					factor + prime
                     while x in factor_map:
                            x += factor
                     lowercase__      =					factor
              else:
                     lowercase__      =					prime
                     yield prime
              prime += 1

def _SCREAMING_SNAKE_CASE (A = 1E10			)			->			int:






       """simple docstring"""







       lowercase__      =					sieve()

       lowercase__      =					1
       while True:
              lowercase__      =					next(A			)
              if (2 * prime * n) > limit:
                     return n
              # Ignore the next prime as the reminder will be 2.
              next(A			)
              n += 2


if __name__ == "__main__":
 print(solution())








'''simple docstring'''

from math import sqrt

def _SCREAMING_SNAKE_CASE (A = 1_000_000			)			->			int:






       """simple docstring"""







       lowercase__      =					0
       lowercase__      =					0
       lowercase__      =					42

       while num_cuboids <= limit:
              max_cuboid_size += 1
              for sum_shortest_sides in range(2    ,					2 * max_cuboid_size + 1			):
                     if sqrt(sum_shortest_sides**2 + max_cuboid_size**2			).is_integer():
                            num_cuboids += (
                                min(A    ,					sum_shortest_sides // 2			)
                                - max(1    ,					sum_shortest_sides - max_cuboid_size			)
                                + 1
                            )

       return max_cuboid_size


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




