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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author beginner1010
 */
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();
    }

    static class TaskC {
        final int maxPrime = 10000 * 2 + 5;
        boolean[] visit;

        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;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] age = new int[n];
            for (int i = 0; i < n; i++) {
                age[i] = in.nextInt();
            }

            boolean[] prime = new boolean[maxPrime];
            Arrays.fill(prime, true);
            prime[0] = prime[1] = false;
            for (int i = 0; i < maxPrime; i++)
                if (prime[i] == true) {
                    for (int j = i * i; j < maxPrime; j += i) {
                        prime[j] = false;
                    }
                }

            int odd = 0;
            for (int i = 0; i < n; i++) {
                if (age[i] % 2 == 1) odd++;
            }

            int[][] cap = new int[n + 2][n + 2];
            int[][] flow = new int[n + 2][n + 2];

            int source = n;
            int sink = n + 1;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++)
                    if (age[i] % 2 == 1 && prime[age[i] + age[j]] == true) {
                        cap[i][j] = 1;
                    }
                if (age[i] % 2 == 1) cap[source][i] = 2;
                else cap[i][sink] = 2;
            }
            int mxFlow = flow(n + 2, cap, flow, source, sink);
            if (odd * 2 != mxFlow || odd != n - odd) {
                out.println("Impossible");
            } else {
                ArrayList<ArrayList<Integer>> cycles = new ArrayList<>();
                visit = new boolean[n];
                for (int i = 0; i < n; i++)
                    if (visit[i] == false) {
                        int currentIndex = i;
                        int previous = -1;
                        ArrayList<Integer> cycle = new ArrayList<>();
                        do {
                            cycle.add(currentIndex + 1);
                            visit[currentIndex] = true;
                            for (int j = 0; j < n; j++) {
                                if (j != previous) {
                                    if (age[currentIndex] % 2 == 0 && flow[j][currentIndex] == 0) continue;
                                    if (age[currentIndex] % 2 == 1 && flow[currentIndex][j] == 0) continue;
                                    previous = currentIndex;
                                    currentIndex = j;
                                    break;
                                }
                            }
                        } while (currentIndex != i);
                        cycles.add(cycle);
                    }
                out.println(cycles.size());
                for (ArrayList<Integer> cycle : cycles) {
                    out.print(cycle.size());
                    for (Integer vertex : cycle) {
                        out.print(" " + vertex);
                    }
                    out.println();
                }
            }
        }

    }

    static 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());
        }

    }
}