C. Another Permutation Problemtime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAndrey 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).InputEach 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.OutputFor each test case, output a single integer — the maximum cost among all permutations of length n.ExampleInput
52431020Output
2
17
7
303
2529
NoteIn 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.
52431020
2 17 7 303 2529 
['brute force', 'dp', 'greedy', 'math', '*1200']