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	pb			push_back
#define	rep(i,n)	for(int i=0;i<n;i++)

using namespace std;

typedef	vector<int>	vi;

int main(){
	const int Ne=1299910;
	static bool er[Ne]; er[0]=er[1]=true;
	for(int i=2;i*i<Ne;i++) if(!er[i]) for(int j=i*i;j<Ne;j+=i) er[j]=true;
	vi p; rep(i,Ne) if(!er[i]) p.pb(i);

	for(int n;scanf("%d",&n),n;){
		vi::iterator itl=lower_bound(p.begin(),p.end(),n),itu=upper_bound(p.begin(),p.end(),n);
		printf("%d\n",*itl-*(itu-1));
	}

	return 0;
}