Double Squares

Description

A double-square number is an integer X which can be expressed as the sum of two perfect squares. For example, 10 is a double-square because $10 = 3^2 + 1^2$. Your task in this problem is, given X, determine the number of ways in which it can be written as the sum of two squares. For example, 10 can only be written as $3^2 + 1^2$ (we don't count $1^2 + 3^2$ as being different). On the other hand, 25 can be written as $5^2 + 0^2$ or as $4^2 + 3^2$.

Input format

You should first read an integer N, the number of test cases. The next N lines will contain N values of X. Constraints 0 ≤ X ≤ 2147483647 1 ≤ N ≤ 100

Output format

For each value of X, you should output the number of ways to write X as the sum of two squares.

Input Sample 1

5
10
25
3
0
1

Output Sample 1

Case #1: 1
Case #2: 2
Case #3: 0
Case #4: 1
Case #5: 1