Couple Destroyer Minuk (Large)

Minuk, who is single, dislikes seeing couples together. He finds a waiting line of $N$ people standing in a row. He plans to split this line into $M$ groups and reorder the groups so that no couple is adjacent. The groups do not need to have the same size. However, the people inside a group cannot be reordered or reversed.

Minuk wants $M$ to be as small as possible, because a large $M$ makes reordering the groups a headache. Let $C$ be the number of valid ways when $M$ is minimal. He wants to find $\min (C, 100)$ of these ways, chosen arbitrarily. Two ways count as different if the group order differs, even when all groups have the same size. Two ways with the same group order also count as different if any group has a different size.

The first line contains an integer $N$ ($1 \le N \le 10^{3}$), the number of people.

The second line contains integers $a_{1}, a_{2}, a_{3}, \cdots, a_{N}$ ($0 \le a_{i} \le 10^{3}$), separated by spaces. $a_{i}$ describes the person at position $i$ from the front of the line. If $a_{i} = 0$, that person is single. If $a_{i} = a_{j}$ and $a_{i} \ne 0$, persons $i$ and $j$ are a couple. Every nonzero value appears exactly twice.

On the first line, print the minimum value of $M$.

From the second line to line $2 \times \min (C, 100) + 1$, print $\min (C, 100)$ valid ways in total.

On line $2k$, print the group sizes for the $k$-th way in the order group 1, group 2, group 3, $\cdots$, group $M$, separated by spaces.

On line $2k + 1$, print the group numbers from the front of the line after the groups are reordered in the $k$-th way.

If $C < 100$, print $-1$ on line $2C + 2$ and print nothing after that.

If no way to split the line into groups and arrange them avoids having at least one couple adjacent, print $-1$ on the first line and print nothing after that.