The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24, 25, 26, 27, 28) between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap contains k.



Input

The input is a sequence of lines each of which contains a single positive integer. Each positive integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709. The end of the input is indicated by a line containing a single zero.

Output

The output should be composed of lines each of which contains a single non-negative integer. It is the length of the prime gap that contains the corresponding positive integer in the input if it is a composite number, or 0 otherwise. No other characters should occur in the output.

Example

Input

10
11
27
2
492170
0


Output

4
0
6
0
114

import java.io.File;
import java.io.FileNotFoundException;
import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.Scanner;

public class Main {
	Scanner sc;

	void run() {

		boolean p[] = new boolean[1300000];
		Arrays.fill(p, true);
		p[0] = false;
		p[1] = false;

		for (int i = 0; i < 1300; i++) {
			if (p[i]) {
				for (int j = i + i; j < 1300000; j += i) {
					p[j] = false;
				}
			}
		}

		LinkedList<Integer> l = new LinkedList<Integer>();
		for (int i = 0; i < 1300000; i++) {
			if (p[i]) {
				l.add(i);
			}
		}

		for (;;) {
			int n = sc.nextInt();

			if (n == 0) {
				break;
			}

			int index = Collections.binarySearch(l, n);
			if(index >= 0){
				System.out.println(0);
			}else{
//				System.out.println(l.get(-index));
//				System.out.println(l.get(-index-1));
				System.out.println(l.get(-index-1) - l.get(-index-2));
			}
		}
	}

	Main() {
		sc = new Scanner(System.in);
		try {
			sc = new Scanner(new File(""));
		} catch (FileNotFoundException e) {
			// TODO Auto-generated catch block
			// e.printStackTrace();
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}
}