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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


public class Main {

    public static long MOD = 1000000007;
    static int[] w, l;
    static int min;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        int[] data = new int[n];
        w = new int[n];
        l = new int[n];
        int odd = 0;
        int even = 0;
        for (int i = 0; i < n; i++) {
            data[i] = in.nextInt();
            if (data[i] % 2 == 0) {
                even++;
            } else {
                odd++;
            }
        }

        HashSet<Integer> set = new HashSet();
        boolean[] p = new boolean[100000];
        for (int i = 2; i < p.length; i++) {
            if (!p[i]) {
                set.add(i);
                for (int j = i + i; j < p.length; j += i) {
                    p[j] = true;
                }
            }
        }
        boolean[][] map = new boolean[n][n];

        for (int i = 0; i < n; i++) {

            for (int j = i + 1; j < n; j++) {
                if (set.contains(data[i] + data[j])) {
                    map[i][j] = true;
                    map[j][i] = true;

                }
            }
        }
        int[][] flow = new int[n + 2][n + 2];
        for (int i = 0; i < n; i++) {
            if (data[i] % 2 == 0) {
                flow[0][i + 1] = 2;
            } else {
                flow[i + 1][n + 1] = 2;
            }
        }
        for (int i = 0; i < n; i++) {
            if (data[i] % 2 == 0) {
                for (int j = 0; j < n; j++) {
                    if (map[i][j]) {
                        flow[i + 1][j + 1] = 1;
                    }
                }
            }
        }
        int result = 0;
        while (true) {
            int[] pa = new int[n + 2];
            Arrays.fill(pa, -1);
            LinkedList<Integer> q = new LinkedList();
            q.add(0);
            pa[0] = 0;
            while (!q.isEmpty()) {
                int node = q.poll();
                for (int i = 1; i < flow.length; i++) {
                    if (flow[node][i] > 0 && pa[i] == -1) {
                        q.add(i);
                        pa[i] = node;
                    }
                }
            }
            //System.out.println(Arrays.toString(pa));
            if (pa[n + 1] == -1) {
                break;
            }
            min = Integer.MAX_VALUE;
            flow(n + 1, pa, flow);
            result += min;
        }
        //System.out.println(result);
        if (result == n) {
            boolean[][] tmp = new boolean[n][n];
            for (int i = 0; i < n; i++) {
                if (data[i] % 2 == 0) {
                    for (int j = 0; j < n; j++) {
                        if (map[i][j] && flow[i + 1][j + 1] == 0) {
                            tmp[i][j] = true;
                            tmp[j][i] = true;
                        }
                    }
                }
            }
            ArrayList<ArrayList<Integer>> re = new ArrayList();
            boolean[] check = new boolean[n];
            for (int i = 0; i < n; i++) {
                if (!check[i] && data[i] % 2 == 0) {
                    check[i] = true;

                    ArrayList<Integer> list = new ArrayList();
                    dfs(i, list, check, tmp);
                    re.add(list);
                }
            }
            out.println(re.size());
            for (ArrayList<Integer> list : re) {
                out.print(list.size() + " ");
                for (int i : list) {
                    out.print((i + 1) + " ");
                }
                out.println();
            }
        } else {
            out.println("Impossible");
        }




        out.close();
    }

    static void dfs(int node, ArrayList<Integer> list, boolean[] check, boolean[][] map) {
        check[node] = true;
        list.add(node);
        for (int i = 0; i < map.length; i++) {
            if (map[node][i] && !check[i]) {
                dfs(i, list, check, map);
            }
        }
    }

    static void flow(int node, int[] pa, int[][] flow) {
        if (pa[node] != node) {
            min = Math.min(min, flow[pa[node]][node]);
            flow(pa[node], pa, flow);
            flow[pa[node]][node] -= min;
            flow[node][pa[node]] += min;
        }
    }

    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;



    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return x - o.x;
        }

        @Override
        public String toString() {
            return "Point{" + "x=" + x + ", y=" + y + '}';
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;


        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}