

'''simple docstring'''







def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     float:

       if edge <= 0 or not isinstance(UpperCAmelCase__,    UpperCAmelCase__			):
              raise ValueError("""Length must be a positive."""			)
       return 3 * ((25 + 10 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)
def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     float:

       if edge <= 0 or not isinstance(UpperCAmelCase__,    UpperCAmelCase__			):
              raise ValueError("""Length must be a positive."""			)
       return ((15 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
      import doctest

      doctest.testmod()



'''simple docstring'''







def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     bool:
       A_		   = len(UpperCAmelCase__			)
       A_		   = [[False] * (required_sum + 1) for _ in range(arr_len + 1			)]

       # for each arr value, a sum of zero(0) can be formed by not taking any element
       # hence True/1
       for i in range(arr_len + 1			):
              A_		   = True

       # sum is not zero and set is empty then false
       for i in range(1,    required_sum + 1			):
              A_		   = False

       for i in range(1,    arr_len + 1			):
              for j in range(1,    required_sum + 1			):
                     if arr[i - 1] > j:
                            A_		   = subset[i - 1][j]
                     if arr[i - 1] <= j:
                            A_		   = subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

       return subset[arr_len][required_sum]


if __name__ == "__main__":
      import doctest

      doctest.testmod()
