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.*;
import java.util.*;
public final class prime_swaps
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static FastScanner sc=new FastScanner(br);
    static PrintWriter out=new PrintWriter(System.out);
	static Random rnd=new Random();
	static List<Integer> list=new ArrayList<Integer>();
	static int[] arr;
	static int maxn=(int)(1e5)+3;
	
	static void mark(int num)
	{
		int i=2,elem;
		while((elem=(num*i))<maxn)
		{
			arr[elem]=1;i++;
		}
	}
	
	static void build()
	{
		arr=new int[maxn];
		for(int i=2;i<maxn;i++)
		{
			if(arr[i]==0)	
			{
				list.add(i-1);mark(i);
			}
		}
	}
	
    public static void main(String args[]) throws Exception
    {
		build();int n=sc.nextInt();int[] a=new int[n],pos=new int[n];List<Pair> al=new ArrayList<Pair>();
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt()-1;pos[a[i]]=i;
		}
		for(int i=0;i<n;i++)
		{
			int diff=Math.abs(i-pos[i]);
			while(diff>0)
			{
				int low=0,high=list.size()-1;
				while(low<high)
				{
					int mid=(low+high+1)>>1;
					if(list.get(mid)<=diff)
					{
						low=mid;
					}
					else
					{
						high=mid-1;
					}
				}
				diff-=list.get(low);
				pos[a[pos[i]-list.get(low)]]=pos[i];
				int temp=a[pos[i]-list.get(low)];
				a[pos[i]-list.get(low)]=a[pos[i]];
				a[pos[i]]=temp;al.add(new Pair(pos[i]-list.get(low),pos[i]));
				pos[i]=pos[i]-list.get(low);
			}
		}
		out.println(al.size());//out.println(Arrays.toString(a));
		for(Pair x:al)
		{
			out.println((x.l+1)+" "+(x.r+1));
		}
		out.close();
    }
}
class Pair
{
	int l,r;
	public Pair(int l,int r)
	{
		this.l=l;this.r=r;
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}