A shrink operation on an array $a$ of size $m$ is defined as follows:

• Choose an index $i$ ($2 \le i \le m - 1$) such that $a_i \gt a_{i - 1}$ and $a_i \gt a_{i + 1}$.
• Remove $a_i$ from the array.

Define the score of a permutation$^{\text{∗}}$ $p$ as the maximum number of times that you can perform the shrink operation on $p$.

Yousef has given you a single integer $n$. Construct a permutation $p$ of length $n$ with the maximum possible score. If there are multiple answers, you can output any of them.

$^{\text{∗}}$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).

Input

The first line of the input contains an integer $t$ ($1 \le t \le 10^3$) — the number of test cases.

Each test case contains an integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the size of the permutation.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output any permutation $p_1, p_2, \dots, p_n$ that maximizes the number of shrink operations.

Note

In the first test case:

• We choose $p = [1, 3, 2]$.
• Choose index $2$, and remove $p_2$ from the array. The array becomes $p = [1, 2]$.

It can be shown that the maximum number of operations we can perform is $1$. Another valid answer is $p = [2, 3, 1]$.

In the second test case:

• We choose $p = [2, 3, 6, 4, 5, 1]$.
• Choose index $5$, and remove $p_5$ from the array. The array becomes $p = [2, 3, 6, 4, 1]$.
• Choose index $3$, and remove $p_3$ from the array. The array becomes $p = [2, 3, 4, 1]$.
• Choose index $3$, and remove $p_3$ from the array. The array becomes $p = [2, 3, 1]$.
• Choose index $2$, and remove $p_2$ from the array. The array becomes $p = [2, 1]$.

The maximum number of operations we can perform is $4$. Any permutation with a score of $4$ is valid.

Samples

2
3
6

1 3 2
2 3 6 4 5 1