Problem Statement

You are given a positive integer $N$.

Find one permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$ that minimizes $\displaystyle \sum_{i=1}^N \bigoplus_{1\le j\le i} P_j$.

Here, $\displaystyle \bigoplus_{1\le j\le i} P_j$ is defined as the bitwise $\mathrm{XOR}$ of $P_1,P_2,\ldots,P_i$.

You are given $T$ test cases; solve each of them.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows. In the binary representation of $A \oplus B$, the digit at the $2^k$ ($k \geq 0$) place is $1$ if exactly one of the digits at the $2^k$ place in the binary representations of $A$ and $B$ is $1$, and $0$ otherwise. For example, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$). In general, the bitwise $\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$, and it can be proved that this does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

Constraints

• $1\le T\le 10^3$
• $1\le N$
• The sum of $N$ over all test cases is at most $2\times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N

Output

Output the answers for the test cases in order, separated by newlines.

For each test case, output a permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$ that minimizes $\displaystyle \sum_{i=1}^N \bigoplus_{1\le j\le i} P_j$, separated by spaces.

If there are multiple permutations $P$ that achieve the minimum, any of them will be accepted.