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.Scanner;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Armenoid
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {

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

    class Edge {
        int to, cap, flow;

        Edge(int to, int cap, int flow) {
            this.to = to;
            this.cap = cap;
            this.flow = flow;
        }
    }

    final int N = 207;
    ArrayList<Integer>[] G = new ArrayList[N];
    ArrayList<Integer>[] graph = new ArrayList[N];
    ArrayList<Edge> edges;
    int n, sink, source;
    int[] dist = new int[N];
    int[] Q = new int[N];
    int[] ptr = new int[N];
    boolean[] used = new boolean[N];

    void addEdge(int u, int v, int cap) {
        G[u].add(edges.size());
        edges.add(new Edge(v, cap, 0));
        G[v].add(edges.size());
        edges.add((new Edge(u, 0, 0)));
    }

    boolean bfs() {

        for (int i = 0; i < n + 2; ++i) {
            dist[i] = -1;
        }
        dist[source] = 0;
        int l = 0, r = 0;
        Q[r++] = source;

        while (l != r) {
            int u = Q[l++];

            for (int id : G[u]) {
                int to = edges.get(id).to;
                int cap = edges.get(id).cap;
                int flow = edges.get(id).flow;
                if (cap != flow && dist[to] == -1) {
                    dist[to] = dist[u] + 1;
                    Q[r++] = to;
                }
            }
        }
        return dist[sink] != -1;
    }

    int dfs(int u, int curFlow) {
        if (u == sink) return curFlow;

        while (ptr[u] != G[u].size()) {

            int id = G[u].get(ptr[u]);
            int to = edges.get(id).to;
            int cap = edges.get(id).cap;
            int flow = edges.get(id).flow;

            if (dist[to] == dist[u] + 1 && flow != cap) {
                int pushed = dfs(to, Math.min(curFlow, cap - flow));
                if (pushed > 0) {
                    edges.get(id).flow += pushed;
                    edges.get(id ^ 1).flow -= pushed;
                    return pushed;
                }
            }

            ++ptr[u];
        }

        return 0;
    }

    void go(int u, ArrayList<Integer> cur) {
        used[u] = true;
        cur.add(u);
        for (int to : graph[u]) {
            if (!used[to]) go(to, cur);
        }
    }

    public void solve(int testNumber, Scanner in, PrintWriter out) {
        n = in.nextInt();
        int[] a = new int[n];

        for (int i = 0; i < n; ++i) {
            a[i] = in.nextInt();
        }

        for (int i = 0; i < n + 2; ++i) {
            G[i] = new ArrayList<Integer>();
            graph[i] = new ArrayList<Integer>();
        }
        edges = new ArrayList<Edge>();

        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (a[i] % 2 == 0 && a[j] % 2 == 1 && isPrime(a[i] + a[j])) {
                    addEdge(i, j, 1);
                }
            }
        }

        source = n;
        sink = n + 1;

        for (int i = 0; i < n; ++i) {
            if (a[i] % 2 == 0) addEdge(source, i, 2);
            else addEdge(i, sink, 2);
        }

        int flow = 0;

        while (bfs()) {

            for (int i = 0; i < n + 2; ++i) {
                ptr[i] = 0;
            }

            while (true) {
                int pushed = dfs(source, Integer.MAX_VALUE);
                if (pushed == 0) break;
                else flow += pushed;
            }
        }

        int cnt = 0;
        for (int i = 0; i < n; ++i) {
            if (a[i] % 2 == 0) ++cnt;
        }

        if (cnt != n - cnt || 2 * cnt != flow) out.println("Impossible");
        else {
            int curId = 0;
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    if (a[i] % 2 == 0 && a[j] % 2 == 1 && isPrime(a[i] + a[j])) {
                        if (edges.get(curId).flow == 1) {
                            graph[i].add(j);
                            graph[j].add(i);
                        }
                        curId += 2;
                    }
                }
            }
            ArrayList<ArrayList<Integer>> ans = new ArrayList<ArrayList<Integer>>();
            for (int i = 0; i < n; ++i) {
                if (!used[i]) {
                    ArrayList<Integer> cur = new ArrayList<Integer>();
                    go(i, cur);
                    ans.add(cur);
                }
            }
            out.println(ans.size());
            for (ArrayList<Integer> mas : ans) {
                out.print(mas.size());
                for (int u : mas) out.print(" " + (u + 1));
                out.println();
            }
        }

    }
}