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.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		boolean[] prime = new boolean[1300000];
		prime[0] = false;
		prime[1] = false;
		for (int i = 2; i < prime.length; i++)
			prime[i] = true;

		for (int i = 0; i < prime.length; i++)
			if (prime[i])
				for (int j = i * 2; j < prime.length; j += i)
					prime[j] = false;

		while (true) {
			int k = sc.nextInt();
			if (k == 0)
				break;
			int l = 0, r = 0;
			for (int i = k; i > 0; i--)
				if (prime[i]) {
					l = i;
					break;
				}
			for (int i = k; i < prime.length; i++)
				if (prime[i]) {
					r = i;
					break;
				}
			int n = r - l;
			System.out.println(n);
		}
		sc.close();
	}
}