A13375 | Board Moves

You are given a board of size $n \times n$ , where $n$ is odd (not divisible by $2$ ). Initially, each cell of the board contains one figure.

In one move, you can select exactly one figure presented in some cell and move it to one of the cells sharing a side or a corner with the current cell, i.e. from the cell $(i, j)$ you can move the figure to cells:

- $(i - 1, j - 1)$ ;
- $(i - 1, j)$ ;
- $(i - 1, j + 1)$ ;
- $(i, j - 1)$ ;
- $(i, j + 1)$ ;
- $(i + 1, j - 1)$ ;
- $(i + 1, j)$ ;
- $(i + 1, j + 1)$ ;

Of course, you can not move figures to cells out of the board. It is allowed that after a move there will be several figures in one cell.

Your task is to find the minimum number of moves needed to get all the figures into one cell (i.e. $n^2-1$ cells should contain $0$ figures and one cell should contain $n^2$ figures).

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 200$ ) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ( $1 \le n < 5 \cdot 10^5$ ) — the size of the board. It is guaranteed that $n$ is odd (not divisible by $2$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$ ( $\sum n \le 5 \cdot 10^5$ ).

For each test case print the answer — the minimum number of moves needed to get all the figures into one cell.