Another Permutation Problem

给定 $n \ (\leqslant 250)$，求一个 $1$ 到 $n$ 的排列 $\{ p_n \}$ 使 $\sum_{i=1}^n p_i \cdot i - \max_{j=1}^n\{ p_j \cdot j \}$ 最大，输出最大值。

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).

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 $ .

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

5
2
4
3
10
20

2
17
7
303
2529

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 $ .