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.util.*;
import java.io.*;
import java.math.*;
public class Main
{
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;} 
        public String s(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();} 
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
        
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = i();}return ret;}
    } 
    
    ///////////////////////////////////////////////////////////////////////////////////////////
    //    RRRRRRRRR            AAA             HHH     HHH     IIIIIIIIIIIII   LLL           //
    //    RR    RRR           AAAAA            HHH     HHH      IIIIIIIIIII    LLL           //
    //    RR   RRR           AAAAAAA           HHH     HHH          III        LLL           //
    //    RR  RRR           AAA   AAA          HHHHHHHHHHH          III        LLL           //
    //    RRRRRR           AAA     AAA         HHHHHHHHHHH          III        LLL           //
    //    RR  RRR         AAAAAAAAAAAAA        HHH     HHH          III        LLL           //
    //    RR    RRR      AAA         AAA       HHH     HHH      IIIIIIIIIII    LLLLLLLLLLLL  //
    //    RR     RRR    AAA           AAA      HHH     HHH     IIIIIIIIIIIII   LLLLLLLLLLLL  //
    ///////////////////////////////////////////////////////////////////////////////////////////
    static class pair 
    {
       int x;
       int y;
       public pair (int k, int p) 
       {
           x = k;
           y = p;
       }
    }
    static boolean prime[]=new boolean[1000001];
    public static void sieve(int n)
    {
        for(int i=0;i<n;i++)
            prime[i] = true;
         
        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p] == true)
            {
                for(int i = p*2; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }
    public static void main(String[] args)throws IOException
    {
        PrintWriter out= new PrintWriter(System.out);
        Reader sc=new Reader();
        int n=sc.i();
        int arr[]=sc.arr(n);
        HashMap<Integer,Integer> hm=new HashMap<Integer,Integer>();
        List<pair>hs=new ArrayList<>();
        sieve(1000000);
        for(int i=0;i<n;i++)hm.put(arr[i],i);
        for(int i=0;i<n;i++)
        {
            if(arr[i]==i+1)
            continue;
            else
            {
                int pos=hm.get(i+1);
                if(prime[pos-i+1])
                {
                    hs.add(new pair(i,pos));
                    int temp=arr[i];
                    arr[i]=arr[pos];
                    arr[pos]=temp;
                    
                    int val1=arr[pos];
                    int val2=arr[i];
                    hm.put(val1,pos);
                    hm.put(val2,i);
                }
                else 
                {
                    for(int j=i+1;;j++)
                    {
                        if(prime[pos-j+1])
                        {
                            hs.add(new pair(j,pos));
                            int temp=arr[j];
                            arr[j]=arr[pos];
                            arr[pos]=temp;
                            
                            int val1=arr[j];
                            int val2=arr[pos];
                            hm.put(val2,pos);
                            hm.put(val1,j);
                            i--;
                            break;
                            
                        }
                    }
                }
            }
            //for(int j=0;j<n;j++)
            //System.out.print(arr[j]+" ");
            //System.out.println();
        }
        out.println(hs.size());
        for(pair p:hs)
        out.println(p.x+1+" "+(p.y+1));
        out.flush();
    } 
}