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 Main {
    IOS ios;
    public static void main(String[] args) throws Exception {
        (new Main()).run();
    }

    void run() throws Exception {
        ios = new IOS("","");
        if (reader() == true) {
            runner();
        } else {
            ios.write("Impossible\n");
        }
        ios.close();
    }

    int n, N;
    int[] a;
    int[][] c;
    boolean reader() throws Exception {
        ios.getToken();
        n = ios.getInt();
        N = n + 1;

        ios.getToken();
        a = new int[N + 1];
        c = new int[N + 1][N + 1];
        int u = 0, v = 0;
        for (int i = 1; i <= n; ++i) {
            a[i] = ios.getInt();
            if (a[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 (a[i] % 2 == 0) {
                for (int j = 1; j <= n; ++j) {
                    if (a[j] % 2 != 0) {
                        boolean IsPrime = true;
                        for (int k = 3; k * k <= a[i] + a[j]; k += 2) {
                            if ((a[i] + a[j]) % k == 0) {
                                IsPrime = false;
                                break;
                            }
                        }
                        //if (a[i] + a[j] == 15) ios.write(IsPrime + "Hi\n");
                        if (IsPrime == true) {
                            c[i][j] = 1;
                        }
                    }
                }
            }
        }
        return true;
    }

    int[] mom;
    int[][] f;
    boolean runner() throws Exception {
        mom = new int[N + 1];
        f = new int[N + 1][N + 1];
        Arrays.fill(mom, -1);
        while (FindPath(0)) {
            IncFlow();
            Arrays.fill(mom, -1);
        }
        int sum = 0;
        for (int i = 1; i <= N; ++i) {
            if (f[0][i] > 0) {
                sum += f[0][i];
            }
        }
        if (sum != n) {
            ios.write("Impossible\n");
            return false;
        }
        Arrays.fill(mom, -1);
        int m = 0;
        ArrayList<ArrayList<Integer>> A = new ArrayList<>();
        for (int i = 1; i <= n; ++i) {
            if (mom[i] == -1) {
                int u = i, v;
                mom[u] = 0;
                A.add(new ArrayList<>());
                A.get(m).add(i);
                while (true) {
                    v = -1;
                    for (int j = 1; j <= n; ++j) {
                        if (mom[j] == -1 && (f[u][j] == 1 || f[j][u] == 1) && (c[u][j] == 1 || c[j][u] == 1)) {
                            v = j;
                            break;
                        }
                    }
                    //if (u == 10) ios.write(v + "Hello\n");
                    if (v == -1) {
                        break;
                    }
                    A.get(m).add(v);
                    mom[v] = u;
                    u = v;
                }
                ++m;
            }
        }
        ios.write(m + "\n");
        for (int i = 0; i < m; ++i) {
            ios.write(A.get(i).size() + " ");
            for (int j: A.get(i)) {
                ios.write(j + " ");
            }
            ios.write("\n");
        }
        return true;
    }
    boolean FindPath(int i) {
        for (int j = 1; j <= N; ++j) {
            if (mom[j] == -1 && c[i][j] > f[i][j]) {
                mom[j] = i;
                if (j == N || FindPath(j) == true) {
                    return true;
                }
            }
        }
        return false;
    }
    void IncFlow() {
        int delta = 10001000, i, j;
        j = N;
        while (j > 0) {
            i = mom[j];
            if (delta > c[i][j] - f[i][j]) {
                delta = c[i][j] - f[i][j];
            }
            j = i;
        }
        j = N;
        while (j > 0) {
            i = mom[j];
            f[i][j] += delta;
            f[j][i] -= delta;
            j = i;
        }
    }
}

class IOS {
    BufferedReader Reader;
    BufferedWriter Writer;
    public IOS(String inp, String out) throws Exception {
        Reader = new BufferedReader((inp == "")? (new InputStreamReader(System.in)): (new FileReader(inp)));
        Writer = new BufferedWriter((out == "")? (new OutputStreamWriter(System.out)): (new FileWriter(out)));
    }
    public void close() throws Exception {
        Writer.flush();
        if (Reader != null) Reader.close();
        if (Writer != null) Writer.close();
        }

    public String getLine() throws Exception {
        return Reader.readLine();
    }

    StringTokenizer Token;
    public void getToken() throws Exception {
        Token = new StringTokenizer(getLine());
    }

    public int getInt() throws Exception {
        return Integer.parseInt(Token.nextToken());
    }
    public long getLong() throws Exception {
        return Long.parseLong(Token.nextToken());
    }

    public void write(String mess) throws Exception {
        Writer.write(mess);
    }
}