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
#include <cstdio>
#define MAX (2000000)
using namespace std;

bool prime[MAX + 1];

int main()
{
	for (int i = 2; i <= MAX; i++){
		prime[i] = true;
	}
	
	for (int i = 2; i * i <= MAX; i++){
		for (int j = i * i; j <= MAX; j += i){
			prime[j] = false;
		}
	}
	
	int n;
	while (scanf("%d", &n), n){
		bool *p;
		int cnt = 0;
		
		p = &prime[n];
		while (*p == false){
			cnt++;
			p--;
		}
		
		p = &prime[n];
		while (*p == false){
			cnt++;
			p++;
		}
		
		printf("%d\n", cnt);
	}
	
	return 0;
}