





from math import sqrt




def     __UpperCamelCase						(_SCREAMING_SNAKE_CASE = 1000000	)       ->     int:
  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(UpperCAmelCase__	,		sum_shortest_sides // 2	)
            - max(1	,		sum_shortest_sides - max_cuboid_size	)
            + 1
        )

  return max_cuboid_size


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








class        SCREAMING_SNAKE_CASE     :  # Public class to implement a graph


   def __init__(					self    :       int    ,  a    :       int    ,  a    :       int    ,  a    :       list[list[bool]] )->     None:





     """simple docstring"""







     lowercase__			    =						row
     lowercase__			    =						col
     lowercase__			    =						graph


   def  SCREAMING_SNAKE_CASE_							(					self    :       Dict    ,  a    :       int    ,  a    :       int    ,  a    :       list[list[bool]] )->     bool:





     """simple docstring"""







     return (
         0 <= i < self.ROW
         and 0 <= j < self.COL
         and not visited[i][j]
         and self.graph[i][j]
     )


   def  SCREAMING_SNAKE_CASE_							(					self    :       List[str]    ,  a    :       int    ,  a    :       int    ,  a    :       list[list[bool]] )->     None:





     """simple docstring"""







     lowercase__			    =						[-1, -1, -1, 0, 0, 1, 1, 1]  # Coordinate order
     lowercase__			    =						[-1, 0, 1, -1, 1, -1, 0, 1]
     lowercase__			    =						True  # Make those cells visited
     for k in range(8 ):
       if self.is_safe(i + row_nbr[k]    ,  j + col_nbr[k]    ,  a ):
         self.diffs(i + row_nbr[k]    ,  j + col_nbr[k]    ,  a )


   def  SCREAMING_SNAKE_CASE_							(					self    :       List[str] )->     int:  # And finally, count all islands.





     """simple docstring"""







     lowercase__			    =						[[False for j in range(self.COL )] for i in range(self.ROW )]
     lowercase__			    =						0
     for i in range(self.ROW ):
       for j in range(self.COL ):
         if visited[i][j] is False and self.graph[i][j] == 1:
           self.diffs(a    ,  a    ,  a )
           count += 1
     return count


