Project Euler #108: Diophantine reciprocals I

_{This problem is a programming version of Problem 108 from projecteuler.net}

In the following equation are positive integers.

For there are exactly three distinct solutions:

Find the number of distinct solutions for a given value of

Input Format

First line containts i.e. number of testcases, each of the lines contains an integer

Constraints

Output Format

Print the answer for each testcase on a new line.

Sample Input

Sample Output

3
2
3