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 <vector>
#include <algorithm>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
const int c=1300000;
bool prime[c+1];
vector<int> pr;
void makeprime(){
	rep(i,c+1) prime[i]=1;
	prime[0]=0,prime[1]=0;
	for(int i=2;i+i<=c;i++) if(prime[i]) for(int j=2;j*i<=c;j++) prime[i*j]=0;
	rep(i,c+1) if(prime[i]) pr.push_back(i);
}
int main(){
	makeprime();
	while(true){
		int n;
		scanf("%d",&n);
		if(!n) break;
		if(prime[n]){
			printf("0\n");
			continue;
		}
		printf("%d\n",pr[upper_bound(pr.begin(),pr.end(),n)-pr.begin()]-pr[upper_bound(pr.begin(),pr.end(),n)-pr.begin()-1]);
	}
}