


from math import sqrt
def   _UpperCamelCase				(						lowerCAmelCase_ = 1_0_0_0_0_0_0   )						->int:
   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   UpperCAmelCase							=     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(lowerCAmelCase_  ,						sum_shortest_sides // 2   )
                - max(1  ,						sum_shortest_sides - max_cuboid_size   )
                + 1
            )

   return max_cuboid_size


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







from __future__ import annotations
def   _UpperCamelCase				(						lowerCAmelCase_   )						->None:
   create_state_space_tree(lowerCAmelCase_  ,						[]  ,						0  ,						[0 for i in range(len(lowerCAmelCase_   )   )]   )
def   _UpperCamelCase				(						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						)						->None:

   if index == len(lowerCAmelCase_   ):
      print(lowerCAmelCase_   )
      return

   for i in range(len(lowerCAmelCase_   )   ):
      if not index_used[i]:
         current_sequence.append(sequence[i]   )
         UpperCAmelCase							=     True
         create_state_space_tree(lowerCAmelCase_  ,						lowerCAmelCase_  ,						index + 1  ,						lowerCAmelCase_   )
         current_sequence.pop()
         UpperCAmelCase							=     False
__a     =			[3, 1, 2, 4]
generate_all_permutations(sequence)

__a     =			["A", "B", "C"]







generate_all_permutations(sequence_a)



