A very hard mathematic problem

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

  Haoren is very good at solving mathematic problems. Today he is working a problem like this:
  Find three positive integers X, Y and Z (X < Y, Z > 1) that holds
   X^Z + Y^Z + XYZ = K
  where K is another given integer.
  Here the operator “^” means power, e.g., 2^3 = 2 * 2 * 2.
  Finding a solution is quite easy to Haoren. Now he wants to challenge more: What’s the total number of different solutions?
  Surprisingly, he is unable to solve this one. It seems that it’s really a very hard mathematic problem.
  Now, it’s your turn.

Input

  There are multiple test cases.
  For each case, there is only one integer K (0 < K < 2^31) in a line.
  K = 0 implies the end of input.
  

Output

  Output the total number of solutions in a line for each test case.

Sample Input

9 53 6 0

Sample Output

1 1 0   
Hint
9 = 1^2 + 2^2 + 1 * 2 * 2 53 = 2^3 + 3^3 + 2 * 3 * 3

Hint

liuyiding

Source

2012 ACM/ICPC Asia Regional Tianjin Online

提交代码