You have an array a[1], a[2], ..., a[n], containing distinct integers from 1 to n. Your task is to sort this array in increasing order with the following operation (you may need to apply it multiple times):

  * choose two indexes, i and j (1 ≤ i < j ≤ n; (j - i + 1) is a prime number); 
  * swap the elements on positions i and j; in other words, you are allowed to apply the following sequence of assignments: tmp = a[i], a[i] = a[j], a[j] = tmp (tmp is a temporary variable). 



You do not need to minimize the number of used operations. However, you need to make sure that there are at most 5n operations.

Input

The first line contains integer n (1 ≤ n ≤ 105). The next line contains n distinct integers a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ n).

Output

In the first line, print integer k (0 ≤ k ≤ 5n) — the number of used operations. Next, print the operations. Each operation must be printed as "i j" (1 ≤ i < j ≤ n; (j - i + 1) is a prime).

If there are multiple answers, you can print any of them.

Examples

Input

3
3 2 1


Output

1
1 3


Input

2
1 2


Output

0


Input

4
4 2 3 1


Output

3
2 4
1 2
2 4
//package codeforces;

import java.io.*;
import java.util.*;

public class C {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
    StringTokenizer stringTokenizer;

    C() throws IOException {
//        reader = new BufferedReader(new FileReader("bridges.in"));
//        writer = new PrintWriter(new FileWriter("bridges.out"));
    }

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    void solve() throws IOException {
        int n = nextInt();
        final int[] a = new int[n + 1];
        final int[] pos = new int[n + 1];
        for(int i = 1; i <= n; i++) {
            a[i] = nextInt();
            pos[a[i]] = i;
        }
        class Utils {
            void swapTo(int what, int where) {
                int x = what;
                int y = a[where];
                int xpos = pos[x];
                int ypos = pos[y];
                swap(a, xpos, ypos);
                swap(pos, x, y);
            }
            void swap(int[] array, int i, int j) {
                int t = array[i];
                array[i] = array[j];
                array[j] = t;
            }
        }
        boolean[] isPrime = new boolean[n + 1];
        Arrays.fill(isPrime, true);
        for(int i = 2; i * i <= n; i++) {
            if(isPrime[i]) {
                for(int j = i * i; j <= n; j += i) {
                    isPrime[j] = false;
                }
            }
        }
        class Swap {
            int i, j;

            Swap(int i, int j) {
                this.i = i;
                this.j = j;
            }

            @Override
            public String toString() {
                return String.format("%d %d", i, j);
            }
        }
        List<Swap> answer = new ArrayList<>(5 * n);
        Utils utils = new Utils();
        for(int i = 1; i <= n; i++) {
            while(i != pos[i]) {
                int dist = pos[i] - i;
                while(!isPrime[dist + 1]) {
                    dist--;
                }
                answer.add(new Swap(pos[i] - dist, pos[i]));
                utils.swapTo(i, pos[i] - dist);
            }
        }
        writer.println(answer.size());
        for (Swap swap : answer) {
            writer.println(swap);
        }
        writer.close();
    }

    public static void main(String[] args) throws IOException {
        new C().solve();
    }
}
