Board Moves

1000ms

262144K

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.

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.

Sample Input:

Sample Output:

0
40
41664916690999888

Informação

Provedor Codeforces

Código CF1353C