You are given an integer $n$. Construct a permutation$^{\text{∗}}$ $p$ of length $n$ satisfying the following condition:

• $\lvert p_i - p_{i+1} \rvert$ is divisible by $i$ for every $1 \le i \le n-1$.

It can be proven that such a permutation always exists under the constraints of the problem.

$^{\text{∗}}$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

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.

The only line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the permutation $p$ to be constructed.

Output

For each test case, output $n$ integers $p_1,p_2,\ldots,p_n$ ($1 \le p_i \le n$, all $p_i$-s are distinct) — the permutation you constructed.

If there are multiple valid permutations, you may output any of them.

Note

In the first test case, $p=[1,2]$ satisfies the condition because $\lvert p_1-p_2\rvert=\lvert 1-2\rvert=1$, which is divisible by $1$.

In the second test case, $p=[2,3,1]$ satisfies the condition because:

• $\lvert p_1-p_2\rvert=\lvert 2-3\rvert=1$, which is divisible by $1$, and
• $\lvert p_2-p_3\rvert=\lvert 3-1\rvert=2$, which is divisible by $2$.

Samples

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