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G. Mexy Permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

For a permutation $$$p$$$ of size $$$n$$$, define the array $$$a$$$ of size $$$n - 1$$$ as the difference array,in other words $$$(a_i = p_i - p_{i-1})$$$ for each $$$(1 \lt i \lt = n)$$$.

A permutation $$$p$$$ is $$$\it{Mexy}$$$ if the $$$mex$$$ of the difference array $$$a$$$ is greater than or equal to $$$\lfloor \frac{2n}{3} \rfloor$$$.

The $$$mex$$$ of an array is the smallest $$$\bf{positive}$$$ integer $$$x$$$ that does not exist in the array.

For example: if we have the permutation $$$p = (1,3,2)$$$, then the difference array $$$a = (2,-1)$$$ and the $$$mex$$$ of array $$$a$$$ is 1.

Given an integer $$$n$$$, find any $$$\it{Mexy}$$$ permutation $$$p$$$ of size $$$n$$$.

Note that you don't have to find the permutation with the maximum $$$mex$$$ value of array $$$a$$$, just find any $$$\it{Mexy}$$$ permutation.

Input

The first line of the input contains a single integer $$$t$$$ $$$(1 \le t \le 10^5)$$$, the number of test cases.

Each test case contains a single line with a single positive integer $$$n$$$ $$$(1 \le n \le 10^5)$$$, the size of the permutations $$$p$$$.

It is guaranteed there is at least one $$$\it{Mexy}$$$ permutation of size $$$n$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$10^5$$$.

Output

For each test case print any $$$\it{Mexy}$$$ permutation of size $$$n$$$.

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