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.Arrays;
import java.util.ArrayList;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.List;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}
 
class TaskC {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; ++i) a[i] = in.nextInt();
        boolean[] prime = new boolean[(int) 2e4 + 1];
        Arrays.fill(prime, 2, prime.length, true);
        for (int i = 2; i < prime.length; ++i) if (prime[i]) {
            for (int j = i * i; j < prime.length; j += i) prime[j] = false;
        }
        int[][] c = new int[n + 2][n + 2];
        int s = n;
        int t = n + 1;
        for (int i = 0; i < n; ++i) {
            if (a[i] % 2 == 0) {
                c[s][i] = 2;
            } else {
                c[i][t] = 2;
            }
            for (int j = 0; j < n; ++j) if (prime[a[i] + a[j]]) {
                if (a[i] % 2 == 0) c[i][j] = 1; else c[j][i] = 1;
            }
        }
        int[][] f = new int[n + 2][n + 2];
        if (flow(n + 2, c, f, s, t) != n) {
            out.println("Impossible");
        } else {
            List<List<Integer>> cycles = new ArrayList<>();
            boolean[] mark = new boolean[n];
            for (int i = 0; i < n; ++i) if (!mark[i]) {
                List<Integer> cycle = new ArrayList<>();
                int cur = i;
                outer: while (true) {
                    mark[cur] = true;
                    cycle.add(cur + 1);
                    for (int j = 0; j < n; ++j) if (f[cur][j] != 0 && !mark[j]) {
                        cur = j;
                        continue outer;
                    }
                    break;
                }
                cycles.add(cycle);
            }
            out.println(cycles.size());
            for (List<Integer> cycle : cycles) {
                out.print(cycle.size());
                for (int x : cycle) out.print(" " + x);
                out.println();
            }
        }
    }
 
    private int flow(int n, int[][] c, int[][] f, int s, int t) {
        boolean[] mark = new boolean[n];
        int res = 0;
        while (dfs(s, t, c, f, mark)) {
            ++res;
            Arrays.fill(mark, false);
        }
        return res;
    }
 
    private boolean dfs(int at, int t, int[][] c, int[][] f, boolean[] mark) {
        if (at == t) return true;
        if (mark[at]) return false;
        mark[at] = true;
        for (int i = 0; i < c.length; ++i) if (f[at][i] < c[at][i] && dfs(i, t, c, f, mark)) {
            ++f[at][i];
            --f[i][at];
            return true;
        }
        return false;
    }
}
 
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
 
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }
 
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }
 
}