B. Permutation
greedy
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 \(i\) \((1 \le i < n)\) such that \(p_i \cdot d = p_{i + 1}\).For example, if \(d = 3\) and \(p = [5, 2, 6, 7, 1, 3, 4]\), 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, then print any of them.
The first line contains a single integer \(t\) (\(1 \le t \le 500\)) — the number of test cases.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 \(2 \cdot 10^5\).
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.