题目描述

For a permutation $p$ of length $n ^{\text{∗}}$ , we define the function:

You are given a number $n$ . You need to compute how many distinct values the function $f(p)$ can take when considering all possible permutations of the numbers from $1$ to $n$ .

$^{\text{∗}}$ 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).

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 500$) — the number of numbers in the permutations.

输出格式

For each test case, output a single integer — the number of distinct values of the function $f(p)$ for the given length of permutations.

输入输出样例 #1

输入 #1

5
2
3
8
15
43

输出 #1

2
3
17
57
463

说明/提示

Consider the first two examples of the input.

For $n = 2$, there are only $2$ permutations — $[1, 2]$ and $[2, 1]$. $ f([1, 2]) = \lvert 1 - 1 \rvert + \lvert 2 - 2 \rvert = 0 $, $ f([2, 1]) = \lvert 2 - 1 \rvert + \lvert 1 - 2 \rvert = 1 + 1 = 2 $. Thus, the function takes $2$ distinct values.

For $n=3$, there are already $6$ permutations: $[1, 2, 3]$, $[1, 3, 2]$, $[2, 1, 3]$, $[2, 3, 1]$, $[3, 1, 2]$, $[3, 2, 1]$, the function values of which will be $0, 2, 2, 4, 4$, and $4$ respectively, meaning there are a total of $3$ values.