P13551 ももいろの鍵

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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.

**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 $n$.

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.

| Subtask | Points | $n \le$ | Special Constraints | | :-: | :-: | :-: | :-: | | $1$ | $10$ | $10$ | None | | $2$ | $10$ | $20$ | None | | $3$ | $15$ | $10^5$ | $\forall n,\exists k \geq 0,k \in \N, n=2^k-1$ | | $4$ | $15$ | $100$ | None | | $5$ | $15$ | $500$ | None | | $6$ | $35$ | $10^5$ | None | 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 $2 \times 10^5$. Generated by Deepseek V3.