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>
#define loop(i,a,b) for(int i=a;i<b;i++)
#define rep(i,a) loop(i,0,a)
using namespace std;

bool prime[2000000];
int gap[1300000];

int main(){
	rep(i,2000000)prime[i]=true;
	prime[0]=prime[1]=false;
	loop(i,2,10000)for(int j=i*2;j<2000000;j+=i)prime[j]=false;
	rep(i,1300000)gap[i]=-1;
	int pre=2;
	loop(i,3,1300000){
		if(prime[i]){
			gap[i]=i-pre;
			pre=i;
		}
	}
	for(int i=1300000-1;i>=2;i--){
		if(gap[i]==-1)gap[i]=pre;
		else{
			pre=gap[i];
			gap[i]=0;
		}
	}
	gap[2]=gap[1]=gap[0]=0;
	int k;
	while(cin>>k,k)cout<<gap[k]<<endl;
	return 0;
}