

'''simple docstring'''







def  UpperCAmelCase__      ( UpperCAmelCase__ = 10_00			)     ->     int:
       A_		   = -1
       A_		   = 0
       for a in range(1,    n // 3			):
              # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
              A_		   = (n * n - 2 * a * n) // (2 * n - 2 * a)
              A_		   = n - a - b
              if c * c == (a * a + b * b):
                     A_		   = a * b * c
                     if candidate >= product:
                            A_		   = candidate
       return product


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



'''simple docstring'''







import math
import sys
def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     int:
       if number != int(UpperCAmelCase__			):
              raise ValueError("""the value of input must be a natural number"""			)
       if number < 0:
              raise ValueError("""the value of input must not be a negative number"""			)
       if number == 0:
              return 1
       A_		   = [-1] * (number + 1)
       A_		   = 0
       for i in range(1,    number + 1			):
              A_		   = sys.maxsize
              A_		   = int(math.sqrt(UpperCAmelCase__			)			)
              for j in range(1,    root + 1			):
                     A_		   = 1 + answers[i - (j**2)]
                     A_		   = min(UpperCAmelCase__,    UpperCAmelCase__			)
              A_		   = answer
       return answers[number]


if __name__ == "__main__":
      import doctest

      doctest.testmod()
