






"""simple docstring"""
from math import sqrt

def        snake_case   (     A__ = 1_00_00_00		):
   UpperCAmelCase_  :				int      =      0
   UpperCAmelCase_  :				int      =      0
   UpperCAmelCase_  :				int

   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() = }')











"""simple docstring"""
from itertools import count

def        snake_case   (     A__ = 50		):
			UpperCAmelCase_  :				Any      =      [1] * min_block_length

			for n in count(A__		):
						fill_count_functions.append(1		)

						for block_length in range(A__			,n + 1		):
									for block_start in range(n - block_length		):
												fill_count_functions[n] += fill_count_functions[
												    n - block_start - block_length - 1
												]

									fill_count_functions[n] += 1

						if fill_count_functions[n] > 1_00_00_00:
									break

			return n


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



