Solve the programming task below in a Python markdown code block.
Given an integer N, find the number of tuples (w, x, y, z) such that 1 ≤ w, x, y, z ≤ N and \frac{w}{x} + \frac{y}{z} is an integer.

For example, if N = 2, the tuple (1,2,1,2) satisfies both conditions, i.e. \frac{1}{2} + \frac{1}{2} = 1 is an integer, however (1,1,1,2) does not since \frac{1}{1} + \frac{1}{2} = 1.5 is not an integer.

------ Input Format ------ 

- The first line of input contains an integer T, denoting the number of test cases. The description of T test cases follows.
- Each test case consists of a single line of input containing one integer, N.

------ Output Format ------ 

- For each test case, print a new line containing a single integer, the answer to that test case.

------ Constraints ------ 

$1 ≤ T ≤ 150$
$1 ≤ N ≤ 1000$
- The sum of $N$ over all test cases does not exceed $10^{4}$

----- Sample Input 1 ------ 
3
2
3
7
----- Sample Output 1 ------ 
10
31
355

----- explanation 1 ------ 

Test Case $1$: There are $2^{4} = 16$ tuples to consider, out of them the only ones that are invalid are those where one of the fractions is $\frac{1}{2}$ and the other is an integer.
The valid tuples are $\{(1, 1, 1, 1), (1, 1, 2, 1), (1, 1, 2, 2), (1, 2, 1, 2), (2, 1, 1, 1), (2, 1, 2, 1), (2, 1, 2, 2), (2, 2, 1, 1), (2, 2, 2, 1), (2, 2, 2, 2)\}$.

Test Cases $2$ and $3$: There are too many tuples to list them in these cases. However, you may verify that among the $3^{4} = 81$ and $7^{4} = 4901$ tuples respectively only $31$ and $355$ of them satisfy the conditions in the problem statement.