AND Minimum Spanning Tree

You are given a complete graph with N vertices, numbered from 1 to N.
The weight of the edge between vertex x and vertex y (1<=x, y<=N, x!=y) is simply the bitwise AND of x and y. Now you are to find minimum spanning tree of this graph.

The first line of the input contains an integer T (1<= T <=10), the number of test cases. Then T test cases follow. Each test case consists of one line containing an integer N (2<=N<=200000).

For each test case, you must output exactly 2 lines. You must print the weight of the minimum spanning tree in the 1st line. In the 2nd line, you must print N-1 space-separated integers f2, f3, … , fN, implying there is an edge between i and fi in your tree(2<=i<=N). If there are multiple solutions you must output the lexicographically smallest one. A tree T1 is lexicographically smaller than tree T2, if and only if the sequence f obtained by T1 is lexicographically smaller than the sequence obtained by T2.

2
3
2

1
1 1
0
1

In the 1st test case, w(1, 2) = w(2, 1) = 0, w(1, 3) = w(3, 1) = 1, w(2, 3) = w(3, 2) = 2. There is only one minimum spanning tree in this graph, i.e. {(1, 2), (1, 3)}.
For the 2nd test case, there is also unique minimum spanning tree.

2019 Multi-University Training Contest 4