A9858 | Fox And Dinner

Fox Ciel is participating in a party in Prime Kingdom. There are $n$ foxes there (include Fox Ciel). The i-th fox is $a_{i}$ years old.

They will have dinner around some round tables. You want to distribute foxes such that:

1. Each fox is sitting at some table.
2. Each table has at least 3 foxes sitting around it.
3. The sum of ages of any two adjacent foxes around each table should be a prime number.

If $k$ foxes $f_{1}$ , $f_{2}$ , ..., $f_{k}$ are sitting around table in clockwise order, then for $1<=i<=k-1$ : $f_{i}$ and $f_{i+1}$ are adjacent, and $f_{1}$ and $f_{k}$ are also adjacent.

If it is possible to distribute the foxes in the desired manner, find out a way to do that.

The first line contains single integer $n$ ( $3<=n<=200$ ): the number of foxes in this party.

The second line contains $n$ integers $a_{i}$ ( $2<=a_{i}<=10^{4}$ ).

If it is impossible to do this, output "Impossible".

Otherwise, in the first line output an integer $m$ (): the number of tables.

Then output $m$ lines, each line should start with an integer $k$ -=– the number of foxes around that table, and then $k$ numbers — indices of fox sitting around that table in clockwise order.

If there are several possible arrangements, output any of them.