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 <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<(n);i++)
#define MP make_pair
#define PB push_back
typedef long long ll;
const int N_MAX=1300000;
bool prime[N_MAX];
int main(){
	int n;
	rep(i,N_MAX)prime[i]=true;
	prime[0]=prime[1]=false;
	rep(i,N_MAX)if(prime[i])for(int j=i*2;j<N_MAX;j+=i)prime[j]=false;
	while(cin>>n,n){
		int i,j;
		for(i=n;!prime[i];i--);
		for(j=n;!prime[j];j++);
		cout<<j-i<<endl;
	}
	return 0;
}