

"""simple docstring"""



def  _snake_case     (    UpperCAmelCase_  :					int = 1000			):
     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  _snake_case     (    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()






