Average Permutation

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.

is minimized.

If multiple permutations are possible, print any of them.

Input

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

The first and only line of each test case contains an integer $n(3\le n\le 10^5)$, 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:

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