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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;

/**
 *
 * @author Mbt
 */
public class C {

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

class Solver{
    final int MAXN= 100001;
    int[] numbers= new int[MAXN];
    int[] positions= new int[MAXN];
    
    byte[] primes= new byte[MAXN+3];
    TreeSet<Integer> primesTree= new TreeSet<>();
    
    void solve() throws IOException{
        BufferedReader reader= new BufferedReader(new InputStreamReader(System.in));
        int n= Integer.valueOf(reader.readLine());
        
        Eratosthenes(MAXN+1);
        
        StringTokenizer st= new StringTokenizer(reader.readLine());
        int index=0;
        while(st.hasMoreTokens()){
            numbers[++index]= Integer.valueOf(st.nextToken());
            positions[numbers[index]]= index;
        }
        
        StringBuilder buffer= new StringBuilder();
        int exCount=0;
        // move each number to it's final position
        while(true){
            boolean nothing= true;
            for (int i=1; i<=n; i++){
                int finalDiff= positions[i]-i+1;
                while(finalDiff>1){
                    // find closest prime number to finalDiff
                    int closestPrime= primesTree.floor(finalDiff);
                    int currDiff= positions[i]-closestPrime+1;
                    exCount++;
                    buffer.append(String.format("%d %d\n", currDiff, positions[i]));
                    
                    int temp= numbers[currDiff];
                    numbers[currDiff]= numbers[positions[i]];
                    numbers[positions[i]]= temp;
                    
                    positions[numbers[positions[i]]]=positions[i];
                    positions[i]= currDiff;
                    
                    finalDiff= finalDiff-closestPrime+1;
                }
            }
            if (nothing) break;
        }
        System.out.println(exCount);
        System.out.print(buffer.toString());
    }
    
    void Eratosthenes(int n){ 
        int limit= (int) Math.sqrt((double)n); 
        int coeff_limit=0; 
 
        int curr_prime=2; 
        while(curr_prime<= limit){ 
            primes[curr_prime]=1; 
            primesTree.add(curr_prime);
            coeff_limit= n/curr_prime; 
 
            // remove coefficient of current prime 
            for (int i=curr_prime; i<=coeff_limit; i++) 
              primes[i*curr_prime]=2; 
 
            // find next prime 
            for (int i=curr_prime+1; i<=n; i++) 
              if (primes[i]==0){ 
                    curr_prime=i; 
                    break; 
              } 
        } 
 
        // mark remained numbers as prime 
        for (int i=curr_prime; i<=n; i++)
            if (primes[i]==0) {
              primes[i]= 1; 
              primesTree.add(i);
            }
    }     
}

class Pair{
    public int x, y;
    public Pair(int x, int y){
        this.x=x; this.y=y;
    }
}