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