This problem is a programming version of Problem 251 from projecteuler.net
A triplet of positive integers is called a Cardano Triplet if it satisfies the condition:
For example, is a Cardano Triplet.
There exist Cardano Triplets for which .
Find how many Cardano Triplets exist such that .
Input Format
The first line of each test file contains a single integer , which is the number of queries. lines follow, each containing the corresponding .
Constraints
OR
OR
Output Format
Print exactly lines with the answer to the corresponding query on each one.
Sample Input 0
2
8
1000
Sample Output 0
1
149
Explanation 0
is the only triplet with the sum .
Sample Input 1
2
999999069
999999550
Sample Output 1
172332336
172332416