Fox And Dinner

2000ms

262144K

Description:

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:

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

If k foxes f₁, f₂, ..., f_k are sitting around table in clockwise order, then for 1 ≤ i ≤ k - 1: f_i and f_i + 1 are adjacent, and f₁ 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.

Input:

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 ≤ 10⁴).

Output:

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

Otherwise, in the first line output an integer m ( $\text{[math]}$ ): 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.

Sample Input:

4
3 4 8 9

Sample Output:

1
4 1 2 4 3

Sample Input:

5
2 2 2 2 2

Sample Output:

Impossible

Sample Input:

12
2 3 4 5 6 7 8 9 10 11 12 13

Sample Output:

1
12 1 2 3 6 5 12 9 8 7 10 11 4

Sample Input:

24
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Sample Output:

3
6 1 2 3 6 5 4
10 7 8 9 12 15 14 13 16 11 10
8 17 18 23 22 19 20 21 24

Note:

In example 1, they can sit around one table, their ages are: 3-8-9-4, adjacent sums are: 11, 17, 13 and 7, all those integers are primes.

In example 2, it is not possible: the sum of 2+2 = 4 is not a prime number.

Informação

Provedor Codeforces

Código CF510E