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# [Solution] Permutation Codeforces Solution | Codeforces 2022

B. Permutation
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Recall that a permutation of length $n$ is an array where each element from $1$ to $n$ occurs exactly once.

For a fixed positive integer $d$, let's define the cost of the permutation $p$ of length $n$ as the number of indices $i$ $\left(1\le i such that ${p}_{i}\cdot d={p}_{i+1}$.

For example, if $d=3$ and $p=\left[5,2,6,7,1,3,4\right]$, then the cost of such a permutation is $2$, because ${p}_{2}\cdot 3={p}_{3}$ and ${p}_{5}\cdot 3={p}_{6}$.

Your task is the following one: for a given value $n$, find the permutation of length $n$ and the value $d$ with maximum possible cost (over all ways to choose the permutation and $d$). If there are multiple answers,

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then print any of them.

Input

The first line contains a single integer $t$ ($1\le t\le 500$) — the number of test cases.

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The single line of each test case contains a single integer $n$ ($2\le n\le 2\cdot {10}^{5}$).

The sum of $n$ over all test cases does not exceed $2\cdot {10}^{5}$.

Output

For each test case, print the value $d$ in the first line, and $n$ integers in the second line — the permutation itself. If there are multiple answers, then print any of them.