# Average Permutation

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

Find a permutation $P=[p_{1},p_{2},...,p_{n}]$ of the integers ${1,2,...,n}$ such that sum of averages of all consecutive triplets is minimized, i.e.

$i=1∑n−2 3p_{i}+p_{i+1}+p_{i+2} $

is minimized.

If multiple permutations are possible, print any of them.

## Input

The first line contains the number of test cases $t(t≤1000)$.

The first and only line of each test case contains an integer $n(3≤n≤10_{5})$, the size of the permutation.

## Output

For each test case, print on a new line any permutation which satisfies the above conditions.

## Examples

The first test case. Among all possible permutations ${3,2,1,4}$ is one which provides the minimum result:

$33+2+1 +32+1+4 =36 +37 =313 =4.3333...$

The second test case. Every permutation of size $3$ will have the same value:

$33+2+1 =36 =2$

Input #1

Answer #1

Submissions 14

Acceptance rate 57%