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.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class Input_3 {
 
    int[] mytab;
    int[][] f;
    int n, N;
    int[] M;
    int[][] C;
    
    
    public static void main(String[] args) throws Exception
    {
        Input_3 op = new Input_3();
        op.run();
    }

    void run() throws Exception 
    {
        if (myReaderFunction() == true)
        {
            myRunnerFunction();
        } else {
            System.out.println("Impossible\n");
        }
        
    }

    
    boolean myReaderFunction() throws Exception 
    {
        Scanner x = new Scanner(System.in);
        
        n = x.nextInt();
        N = n + 1;

        
        M = new int[N + 1];
        C = new int[N + 1][N + 1];
        int u = 0, v = 0;
        for (int i = 1; i <= n; ++i) 
        {
            M[i] = x.nextInt();
            if (M[i] % 2 == 0)
            {
                ++u;
                C[0][i] = 2;
            } else {
                ++v;
                C[i][N] = 2;
            }
        }
        if (u != v) {
            return false;
        }
        for (int i = 1; i <= n; ++i) {
            if (M[i] % 2 == 0)
            {
                for (int j = 1; j <= n; ++j) 
                {
                    if (M[j] % 2 != 0) 
                    {
                        boolean IsPrime = true;
                        for (int k = 3; k * k <= M[i] + M[j]; k += 2)
                        {
                            if ((M[i] + M[j]) % k == 0)
                            {
                                IsPrime = false;
                                break;
                            }
                        }
                        
                        if (IsPrime == true)
                        {
                            C[i][j] = 1;
                        }
                    }
                }
            }
        }
        return true;
    }

   
    
    boolean myRunnerFunction() throws Exception 
    {
        mytab = new int[N + 1];
        f = new int[N + 1][N + 1];
        Arrays.fill(mytab, -1);
        
        while (Find(0)) 
        {
            Flow();
            Arrays.fill(mytab, -1);
        }
        int sum = 0;
        for (int i = 1; i <= N; ++i)
        {
            if (f[0][i] > 0)
            {
                sum += f[0][i];
            }
        }
        if (sum != n) 
        {
            System.out.println("Impossible\n");
            return false;
        }
        Arrays.fill(mytab, -1);
        int m = 0;
        ArrayList<ArrayList<Integer>> A = new ArrayList<>();
        
        for (int i = 1; i <= n; ++i) 
        {
            if (mytab[i] == -1) 
            {
                int u = i, v;
                mytab[u] = 0;
                A.add(new ArrayList<Integer>());
                A.get(m).add(i);
                
                while (true) 
                {
                    v = -1;
                    for (int j = 1; j <= n; ++j) 
                    {
                        if (mytab[j] == -1 && (f[u][j] == 1 || f[j][u] == 1) && (C[u][j] == 1 || C[j][u] == 1)) 
                        {
                            v = j;
                            break;
                        }
                    }
                   
                    if (v == -1) 
                    {
                        break;
                    }
                    
                    A.get(m).add(v);
                    mytab[v] = u;
                    u = v;
                }
                ++m;
            }
        }
        System.out.println(m + "\n");
        for (int i = 0; i < m; ++i)
        {
            System.out.println(A.get(i).size() + " ");
            for (int j: A.get(i))
            {
                System.out.println(j + " ");
            }
            System.out.println("\n");
        }
        return true;
    }
    
    
    boolean Find(int i) 
    {
        for (int j = 1; j <= N; ++j) 
        {
            if (mytab[j] == -1 && C[i][j] > f[i][j])
            {
                mytab[j] = i;
                if (j == N || Find(j) == true) 
                {
                    return true;
                }
            }
        }
        return false;
    }
    
    
    void Flow() 
    {
        int delta = 10001000, i, j;
        j = N;
        
        while (j > 0) 
        {
            i = mytab[j];
            if (delta > C[i][j] - f[i][j]) 
            {
                delta = C[i][j] - f[i][j];
            }
            j = i;
        }
        
        j = N;
        
        while (j > 0)
        {
            i = mytab[j];
            f[i][j] += delta;
            f[j][i] -= delta;
            j = i;
        }
    }
}