Team Partitioning

There are n children participating in a competition. They are to be divided into several teams. Each child i has a requirement a_i, which means that the team to which child i belongs must have at least a_i members (including himself/herself).

Your task is to produce a partition of the children into teams so that:

• The number of teams is maximized.
• Subject to the maximum number of teams, the largest team size among all teams is minimized.

It is guaranteed that a valid partition exists by possibly leaving out some children (i.e. some children might not be assigned to any team if they cannot be grouped).

Note: The optimal strategy is to greedily form teams using the children with the smallest requirements first. In other words, sort the children by their a_i values, then, iteratively, accumulate children until the current group size is at least as large as the requirement of the most recent child added, form a team, and then start a new group.

This greedy algorithm yields both the maximum number of teams and minimizes the maximum team size.

inputFormat

The first line contains a single integer n (1 ≤ n ≤ 10⁵), the number of children.

The second line contains n integers: a₁, a₂, ..., a_n (1 ≤ a_i ≤ n), where a_i is the minimum required team size for the i-th child.

outputFormat

First, output a single integer T representing the maximum number of teams formed.

Then output T lines, each describing a team. For each team, first output an integer k indicating the number of members in that team, followed by k space-separated integers representing the indices of the children in that team.

If there are multiple valid partitions, output any one of them.

sample

5
2 1 3 2 1

3
1 2
1 5
2 1 4