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.awt.Point;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class Main {

	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok = new StringTokenizer("");

	void init() throws FileNotFoundException {
		if (ONLINE_JUDGE) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		} else {
			in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter("output.txt");
		}
	}

	String readString() throws IOException {
		while (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}

	long readLong() throws IOException {
		return Long.parseLong(readString());
	}

	double readDouble() throws IOException {
		return Double.parseDouble(readString());
	}

	public static void main(String[] args) {
		new Main().run();
		// Sworn to fight and die
	}

	public static void mergeSort(int[] a) {
		mergeSort(a, 0, a.length - 1);
	}

	private static void mergeSort(int[] a, int levtIndex, int rightIndex) {
		final int MAGIC_VALUE = 50;
		if (levtIndex < rightIndex) {
			if (rightIndex - levtIndex <= MAGIC_VALUE) {
				insertionSort(a, levtIndex, rightIndex);
			} else {
				int middleIndex = (levtIndex + rightIndex) / 2;
				mergeSort(a, levtIndex, middleIndex);
				mergeSort(a, middleIndex + 1, rightIndex);
				merge(a, levtIndex, middleIndex, rightIndex);
			}
		}
	}

	private static void merge(int[] a, int levtIndex, int middleIndex,
			int rightIndex) {
		int length1 = middleIndex - levtIndex + 1;
		int length2 = rightIndex - middleIndex;
		int[] levtArray = new int[length1];
		int[] rightArray = new int[length2];
		System.arraycopy(a, levtIndex, levtArray, 0, length1);
		System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
		for (int k = levtIndex, i = 0, j = 0; k <= rightIndex; k++) {
			if (i == length1) {
				a[k] = rightArray[j++];
			} else if (j == length2) {
				a[k] = levtArray[i++];
			} else {
				a[k] = levtArray[i] <= rightArray[j] ? levtArray[i++]
						: rightArray[j++];
			}
		}
	}

	private static void insertionSort(int[] a, int levtIndex, int rightIndex) {
		for (int i = levtIndex + 1; i <= rightIndex; i++) {
			int current = a[i];
			int j = i - 1;
			while (j >= levtIndex && a[j] > current) {
				a[j + 1] = a[j];
				j--;
			}
			a[j + 1] = current;
		}
	}

	public void run() {
		try {
			long t1 = System.currentTimeMillis();
			init();
			solve();
			out.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = " + (t2 - t1));
		} catch (Exception e) {
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}

	class LOL implements Comparable<LOL> {
		int x;
		int ind;
		int ans;

		public LOL(int x, int i) {
			this.x = x;
			this.ind = i;
		}

		@Override
		public int compareTo(LOL o) {

			if (x == o.x)
				return (ind - o.ind);
			return (x - o.x); // ---->
			// return o.x - x; // <----
		}

	}

	boolean prime(int n) {
		for (int i = 2; i <= sqrt(n); i++)
			if (n % i == 0)
				return false;
		return true;
	}

	public void solve() throws IOException {

		int n = readInt();
		boolean[] prost = new boolean[n + 1];
		for (int i = 1; i < n + 1; i++)
			prost[i] = prime(i);
		int[] a = new int[n + 1];
		int[] aa = new int[n + 1];
		int[][] b = new int[500000][2];
		int ans = 0;

		for (int i = 1; i < n + 1; i++) {
			int t = readInt();
			a[t] = i;
			aa[i] = t;
		}

		for (int i = 1; i < n + 1; i++)
			if (a[i] != i) {
				int p = a[i];
				int m = p - i + 1;
				while (!prost[m]) {
					m--;
				}

				b[ans][1] = p;
				b[ans][0] = p - m + 1;
				ans++;
				int tmp = a[aa[p]];
				a[aa[p]] = a[aa[p - m + 1]];
				a[aa[p - m + 1]] = tmp;
				tmp = aa[p];
				aa[p] = aa[p - m + 1];
				aa[p - m + 1] = tmp;
				i--;
			}
		out.println(ans);
		for (int i = 0; i < ans; i++)
			out.println(b[i][0] + " " + b[i][1]);

	}
}
