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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
bool a[1300000]={0};
a[1]=1;
for(int i=2;i<650001;i++){
	if(a[i]==1) continue;
	int j=2*i;
	while(j<1300000){
		a[j]=1;
		j=j+i;
	}
}
int k;
while(cin>>k && k){
int ans;
if(a[k]==0) ans=0; 
else{
	int l=k+1,m=k-1;
	while(a[l]==1) l++;
	while(a[m]==1)  m--;
	ans=l-m;
}
cout<<ans<<endl;

}



	return 0;
}