1391/A A. Suborrays_综合

A. Suborrays

http://codeforces.com/contest/1391/A

题面：

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).

For a positive integer $n$ , we call a permutation $p$ of length $n$ good if the following condition holds for every pair $i$ and $j$ ( $1 \le i \le j \le n$ ) —

$(p_i \text{ OR } p_{i+1} \text{ OR } \ldots \text{ OR } p_{j-1} \text{ OR } p_{j}) \ge j-i+1$ , where $\text{OR}$ denotes the bitwise OR operation.

In other words, a permutation $p$ is good if for every subarray of $p$ , the $\text{OR}$ of all elements in it is not less than the number of elements in that subarray.

Given a positive integer $n$ , output any good permutation of length $n$ . We can show that for the given constraints such a permutation always exists.

Input

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

The first and only line of every test case contains a single integer $n$ ( $1 \le n \le 100$ ).

Output

For every test, output any good permutation of length $n$ on a separate line.

Example

input

output

1
3 1 2
4 3 5 2 7 1 6

Note

For $n = 3$ , $[3,1,2]$ is a good permutation. Some of the subarrays are listed below.

$3\text{ OR }1 = 3 \geq 2$ $(i = 1,j = 2)$

$3\text{ OR }1\text{ OR }2 = 3 \geq 3$ $(i = 1,j = 3)$

$1\text{ OR }2 = 3 \geq 2$ $(i = 2,j = 3)$

$1 \geq 1$ $(i = 2,j = 2)$

Similarly, you can verify that $[4,3,5,2,7,1,6]$ is also good.

翻译：

一个排列permutation长度为 $n$ 是一个数组，组成consisting 是n个不同的整数从 $1$ 到 $n$ 任意arbitrary 顺序 order。例如， $[2,3,1,5,4]$ , 是一个排列，但是 $[1,2,2]$ 不是一个排列（2出现了两次在数组里）并且 $[1,3,4]$ 也不是排列（n = 3 但是这里有 4 在数组里）。

对于正整数 n，我们叫排列 P 长度为 n 是好，如果他以下following 情况condition 保持，对于每一对 $i$ and $j$ ( $1 \le i \le j \le n$ ) — $(p_i \text{ OR } p_{i+1} \text{ OR } \ldots \text{ OR } p_{j-1} \text{ OR } p_{j}) \ge j-i+1$ ,，其中OR代表denotes 按位bitwise OR 运算符 operation 运算

换句话说In other words，P排列是一个好的如果对于每一个子数组subarray 从P中，所有元素的OR不小于元素的数量在子数组中。

给一个正整数 N，输出任意好的排列长度为 n。我们证明show 对于给定的约束constraints ，这样的一个排列总是存在的。

题意：

$(p_i \text{ OR } p_{i+1} \text{ OR } \ldots \text{ OR } p_{j-1} \text{ OR } p_{j}) \ge j-i+1$

给你一个从 1 到 n 的数组，求一个排列，满足上面的式子。

题解：

有个 OR 的规律：
$a \text{ OR } b \ge a + b$
所以任意两个 $OR$ ，一定大于两个数相加。

那么，将数组从 1 到 n 输出，就算每次增加最小的加一，最后也是满足上面的规则。

代码：

#include <bits/stdc++.h>
using namespace std;int main(void)
{int T;cin>>T;while(T--){int n;cin>>n;for(int i=1; i<=n; i++){cout<<i<<" ";}cout<<endl;}return 0;
}