Another Permutation Problem

3000ms

262144K

Description:

Andrey is just starting to come up with problems, and it's difficult for him. That's why he came up with a strange problem about permutations$$$^{\dagger}$$$ and asks you to solve it. Can you do it?

Let's call the cost of a permutation $$$p$$$ of length $$$n$$$ the value of the expression:

$$$(\sum_{i = 1}^{n} p_i \cdot i) - (\max_{j = 1}^{n} p_j \cdot j)$$$.

Find the maximum cost among all permutations of length $$$n$$$.

$$$^{\dagger}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input:

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 30$$$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 250$$$) — the length of the permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output:

For each test case, output a single integer — the maximum cost among all permutations of length $$$n$$$.

Sample Input:

Sample Output:

Note:

In the first test case, the permutation with the maximum cost is $$$[2, 1]$$$. The cost is equal to $$$2 \cdot 1 + 1 \cdot 2 - \max (2 \cdot 1, 1 \cdot 2)= 2 + 2 - 2 = 2$$$.

In the second test case, the permutation with the maximum cost is $$$[1, 2, 4, 3]$$$. The cost is equal to $$$1 \cdot 1 + 2 \cdot 2 + 4 \cdot 3 + 3 \cdot 4 - 4 \cdot 3 = 17$$$.

Informação

Provedor Codeforces

Código CF1859C