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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.List;

public class C {
	InputStream is;
	PrintWriter out;
	String INPUT = "";

	void solve()
	{
		int[] primes = sieveEratosthenes(100000);
		
		int n = ni();
		int[][] a = new int[n][];
		for(int i = 0;i < n;i++){
			a[i] = new int[]{ni(), i};
		}
		Arrays.sort(a, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				return a[0] - b[0];
			}
		});
		int[] ia = new int[n];
		for(int i = 0;i < n;i++)ia[a[i][1]] = i;
		List<String> lines = new ArrayList<String>();
		for(int i = 0;i < n;i++){
			int x = a[i][1];
			while(x > i){
				int ind = Arrays.binarySearch(primes, x-i+1);
				if(ind < 0)ind = -ind-2;
				lines.add((x-primes[ind]+1+1) + " " + (x+1));
				int nex = x-primes[ind]+1;
				int num = ia[nex];
				{int d = a[i][1]; a[i][1] = a[num][1]; a[num][1] = d;}
				{int d = ia[x]; ia[x] = ia[nex]; ia[nex] = d;}
				x = nex;
			}
		}
		out.println(lines.size());
		for(String line : lines){
			out.println(line);
		}
	}
	
	public static int[] sieveEratosthenes(int n) {
		if(n <= 32){
			int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
			for(int i = 0;i < primes.length;i++){
				if(n < primes[i]){
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
		for(int tp : tprimes){
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for(int i = (tp - 3) / 2;i < tp << 5;i += tp)
				ptn[i >> 5] |= 1 << (i & 31);
			for(int i = 0;i < tp;i++){
				for(int j = i;j < sup;j += tp)
					isp[j] |= ptn[i];
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4,
				13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 };
		int h = n / 2;
		for(int i = 0;i < sup;i++){
			for(int j = ~isp[i];j != 0;j &= j - 1){
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if(p > n)
					break;
				ret[pos++] = p;
				for(int q = pp;q <= h;q += p)
					isp[q >> 5] |= 1 << (q & 31);
			}
		}

		return Arrays.copyOf(ret, pos);
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new C().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}