Last Number

2000ms

262144K

Description:

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.

Input:

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 $$$S$$$.

Output:

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

Sample Input:

Sample Output:

Note:

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 $$$2$$$.

Informação

Provedor Codeforces

Código CF1810H