You are given an integer N. You have to count the number of distinct tuples (A, B, C, D) with 1 ≤ A, B, C, D ≤ N such that $A \cdot B = C \cdot D$.

Two tuples, say (A, B, C, D) and (E, F, G, H) are considered to be different if at least one of the following conditions hold true:
$A \neq E$
$B \neq F$
$C \neq G$
$D \neq H$.

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

• First line will contain T, number of testcases. Then the testcases follow.
• Each testcase contains a single integer on a new line - N, as described in the problem statement

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

For each testcase, output the answer on a new line - the number of tuples as described in the problem statement.

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

$1 ≤ T ≤ 10$
$1 ≤ N ≤ 10^{6}$

----- Sample Input 1 ------
3
3
50
35
----- Sample Output 1 ------
15
10950
4831
----- explanation 1 ------
Test case $1$:
Following tuples satisfy the given condition:
- (1, 1, 1, 1)
- (1, 2, 2, 1)
- (1, 3, 3, 1)
- (2, 1, 1, 2)
- (2, 2, 2, 2)
- (2, 3, 3, 2)
- (3, 1, 1, 3)
- (3, 2, 2, 3)
- (3, 3, 3, 3)
- (1, 2, 1, 2)
- (2, 1, 2, 1)
- (1, 3, 1, 3)
- (3, 1, 3, 1)
- (2, 3, 2, 3)
- (3, 2, 3, 2)

$A \cdot B = C \cdot D$ holds true for all these tuples.

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