Problem Statement

You are given a positive integer $N$.

Let $G$ be a complete undirected graph with $N$ vertices $1,2,\ldots,N$ and $\displaystyle \frac{N(N-1)}2$ edges.

Find a trail $(v_1,v_2,\ldots,v_k)$ on $G$ satisfying all of the following conditions.

• for all integers $i$ such that $1 \leq i \leq k-2$, $|v_i - v_{i+2}| = 1$
• $\displaystyle \frac{(N-2)^2}2 \le k$

It can be proved that such a trail always exists under the constraints.

What is a trail? A sequence of vertices $(v_1,v_2,\ldots,v_k)$ on an undirected graph $G$ is called a trail on $G$ if all of the following conditions are satisfied. $1\le v_i\le N.$ For $1\le i\le k-1$, there exists an edge connecting vertices $v_i$ and $v_{i+1}$. For $1\le i < j \le k-1$, the edge connecting vertices $v_i$ and $v_{i+1}$ and the edge connecting vertices $v_j$ and $v_{j+1}$ are distinct.

Constraints

• $1\le T\le 50$
• $3\le N\le 1000$
• The sum of $N$ over all test cases is at most $1000$.
• 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 trail $(v_1,v_2,\ldots,v_k)$ on $G$ satisfying all conditions in the following format:

k
v_1 v_2 \ldots v_k

If multiple trails on $G$ satisfying all conditions exist, any of them will be accepted.