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>
#include <cstring>

bool prime[1300001];

int main(void){
	memset(prime,true,sizeof(prime));
	prime[0]=prime[1]=false;
	for(int i=2;i<=1300000;i++){
		if(prime[i]){
			for(int j=i*2;j<=1300000;j+=i)prime[j]=false;
		}
	}
	while(1){
		int k;
		scanf("%d",&k);
		if(k==0)break;
		if(prime[k]){
			printf("0\n");
			continue;
		}
		int l=k,r=k;
		while(!prime[l])l--;
		while(!prime[r])r++;
		printf("%d\n",r-l);
	}
	return 0;
}