CF1810H.Last Number

普及/提高-

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题目描述

You are given a multiset $S$ . Initially, $S = \{1,2,3, \ldots, n\}$ .

You will perform the following operation $n-1$ times.

Choose the largest number $S_{\text{max}}$ in $S$ and the smallest number $S_{\text{min}}$ in $S$ . Remove the two numbers from $S$ , and add $S_{\text{max}} - S_{\text{min}}$ into $S$ .

It's easy to show that there will be exactly one number left after $n-1$ operations. Output that number.

输入格式

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^5$ ) — the number of test cases. Their description follows.

For each test case, one single line contains a single integer $n$ ( $2 \le n \le 10^9$ ) — the initial size of the multiset $S$ .

输出格式

For each test case, output an integer denoting the only number left after $n-1$ operations.

输入输出样例

输入#1
```
5
2
4
7
15
177567
```
输出#1
```
1
2
2
4
33914
```

说明/提示

We show how the multiset $S$ changes for $n=4$ .

Operation $1$ : $S=\{1,2,3,4\}$ , remove $4$ , $1$ , add $3$ .
Operation $2$ : $S=\{2,3,3\}$ , remove $3$ , $2$ , add $1$ .
Operation $3$ : $S=\{1,3\}$ , remove $3$ , $1$ , add $2$ .
Final: $S = \{2\}$ .

Thus, the answer for $n = 4$ is $2$ .

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