Description

You are given a non-negative integer $n$. You need to partition the numbers $0, 1, 2, \dots, n$ into several groups such that the bitwise AND of all numbers in each group is $0$.

Your goal is to maximize the number of groups and provide a valid partitioning scheme.

Input Format

This problem contains multiple test cases in a single test point.

The first line contains a positive integer $T$, indicating the number of test cases.

For each test case, the input is formatted as follows:

• One line containing a non-negative integer $n$.

Output Format

For each test case, first output a positive integer $ans$, representing the maximum number of groups.

Then, output $ans$ lines. Each line should start with a positive integer $k$, indicating the size of the current group, followed by $k$ integers representing the elements in the group.

If there are multiple optimal partitioning schemes, you may output any of them.

4
0
1
2
3

1
1 0
1
2 0 1
2
2 2 1
1 0
2
2 1 2
2 0 3

Hint

For all test cases, it is guaranteed that $1 \le T \le 600$, $0 \le n \le 10^5$, and the sum of $n$ across all test cases in a single test point does not exceed $2 \times 10^5$.

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