Board Moves
Description
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.
Input
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 $5 \cdot 10^5$ ($\sum n \le 5 \cdot 10^5$).
Output
For each test case print the answer — the minimum number of moves needed to get all the figures into one cell.
Samples
3
1
5
499993
0
40
41664916690999888