Problem: Fox Ciel is participating in a party in Prime Kingdom. There are n foxes there (include Fox Ciel). The i-th fox is ai 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 f1, f2, ..., fk are sitting around table in clockwise order, then for 1 ≤ i ≤ k - 1: fi and fi + 1 are adjacent, and f1 and fk 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 ai (2 ≤ ai ≤ 104).

Output

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

Otherwise, in the first line output an integer m (<image>): 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.

Examples

Input

4
3 4 8 9


Output

1
4 1 2 4 3


Input

5
2 2 2 2 2


Output

Impossible


Input

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


Output

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


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


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.

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class CF290C {
    static int[][] g;
    static boolean[][] g2;
    static boolean[] v;
    static int[] a;

    static int dfs(int i, int d, int f) {
        if (v[i])
            return 0;
        if (i == d)
            return f;
        v[i] = true;
        for (int j = 0; j < g.length; j++) {
            int fl = 0;
            if (g[i][j] != 0 && (fl = dfs(j, d, Math.min(g[i][j], f))) != 0) {
                g[i][j] -= fl;
                g[j][i] += fl;
                return fl;
            }
        }
        return 0;
    }

    static int maxflow(int s, int t) {
        int flow = 0;
        int cfl = 0;
        while ((cfl = dfs(s, t, Integer.MAX_VALUE)) != 0) {
            flow += cfl;
            Arrays.fill(v, false);
        }
        return flow;
    }

    static boolean isPrime(int n) {
        for (int i = 2; i * i <= n; i++)
            if (n % i == 0)
                return false;
        return true;
    }

    static void dfs(int i, ArrayList<Integer> s) {
        if (v[i])
            return;
        v[i] = true;
        s.add(i + 1);
        for (int j = 0; j < g2.length; j++) {
            if (g2[i][j]) {
                dfs(j, s);
            }
        }
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = in.nextInt();
        g = new int[n + 2][n + 2];
        v = new boolean[n + 2];
        for (int i = 0; i < n; i++) {
            if (a[i] % 2 == 0)
                g[0][i + 2] = 2;
            else
                g[i + 2][1] = 2;
            for (int j = 0; j < n; j++)
                if (a[j] % 2 > a[i] % 2 && isPrime(a[i] + a[j]))
                    g[i + 2][j + 2] = 1;
        }

        if (maxflow(0, 1) == n) {
            g2 = new boolean[n][n];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    if (a[j] % 2 > a[i] % 2 && isPrime(a[i] + a[j])
                            && g[i + 2][j + 2] == 0) {
                        g2[i][j] = g2[j][i] = true;
                    }
            ArrayList<ArrayList<Integer>> arr = new ArrayList<ArrayList<Integer>>();
            Arrays.fill(v, false);
            for (int i = 0; i < n; i++) {
                if (!v[i]) {
                    ArrayList<Integer> cycle = new ArrayList<Integer>();
                    dfs(i, cycle);
                    arr.add(cycle);
                }
            }
            System.out.println(arr.size());
            for (ArrayList<Integer> list : arr) {
                System.out.println(list.size() + " "
                        + list.toString().replaceAll("\\[|\\]|,", ""));
            }

        } else {
            System.out.println("Impossible");
        }

    }
}