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>

bool num[2000000];

void prime(){
	num[0] = false;
	num[1] = false;
	for(int i = 2; i < 2000000; i++) num[i] = true;
	for(int i = 2; i < 2000; i++){
		if(!num[i]) continue;
		for(int j = 2*i; j < 2000000; j += i){
			num[j] = false;
		}
	}
}

int main(){
	prime();
	int n;
	while(scanf("%d", &n),n){
		if(num[n]){
			printf("0\n");
			continue;
		}
		int cnt = 0;
		for(int i = 1;;i++){
			if(num[n+i]){
				cnt += i;
				break;
			}
		}
		for(int i = 1;;i++){
			if(num[n-i]){
				cnt += i;
				break;
			}
		}
		printf("%d\n", cnt);
	}
}