K. Xor-permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Sunset Shimmer defines the value of a permutation $$$p$$$ of length $$$n$$$ is $$$\sum_{i=1}^np_i\oplus i$$$, the $$$\oplus$$$ represents bitwise XOR.

Now she wants to know the maximal value of permutation of lenght $$$n$$$.

Input

The first line contains a single integer $$$T\ (1\le T\le 10^5)$$$ - the number of testcases.

Each testcase contains a single integer $$$n(1\le \sum n\le 10^5)$$$ - the length of the permutation.

Output

For each testcase, print one line of $$$n$$$ integers , represents the maximal value permutation of length $$$n$$$.

If there are multiple solutions, just output any of them.

Example
Input
2
3
5
Output
3 1 2
5 1 4 3 2