# Special Triplets solution codechef

## Special Triplets solution codechef

Gintoki has been very lazy recently and he hasn’t made enough money to pay the rent this month. So the old landlady has given him a problem to solve instead, if he can solve this problem the rent will be waived. The problem is as follows:

A triplet of integers (A,B,C)(A,B,C) is considered to be special if it satisfies the following properties for a given integer NN :

• AmodB=CAmodB=C
• BmodC=0BmodC=0
• 1A,B,CN1≤A,B,C≤N

Example: There are three special triplets for N=3N=3.

• (1,3,1)(1,3,1) is a special triplet, since (1mod3)=1(1mod3)=1 and (3mod1)=0(3mod1)=0.
• (1,2,1)(1,2,1) is a special triplet, since (1mod2)=1(1mod2)=1 and (2mod1)=0(2mod1)=0.
• (3,2,1)(3,2,1) is a special triplet, since (3mod2)=1(3mod2)=1 and (2mod1)=0(2mod1)=0.

The landlady gives Gintoki an integer NN. Now Gintoki needs to find the number of special triplets. Can you help him to find the answer?

### Input Format

• The first line of the input contains a single integer TT denoting the number of test cases. The description of TT test cases follows.
• The first and only line of each test case contains a single integer NN.

### Output Format

• For each testcase, output in a single line the number of special triplets.

### Constraints

• 1T101≤T≤10
• 2N1052≤N≤105

Subtask #3 (75 points): Original constraints

### Sample Input 1

3
3
4
5


### Sample Output 1

3
6
9


### Explanation

Test case 11: It is explained in the problem statement.

Test case 22: The special triplets are (1,3,1)(1,3,1)(1,2,1)(1,2,1)(3,2,1)(3,2,1)(1,4,1)(1,4,1)(4,3,1)(4,3,1)(2,4,2)(2,4,2). Hence the answer is 66.

Test case 33: The special triplets are (1,3,1)(1,3,1)(1,2,1)(1,2,1)(3,2,1)(3,2,1)(1,4,1)(1,4,1)(4,3,1)(4,3,1)(1,5,1)(1,5,1)(5,4,1)(5,4,1)(5,2,1)(5,2,1)(2,4,2)(2,4,2). Hence the answer is 99.