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>
#define M 1299709
using namespace std;
void make(vector<bool>& a){
a[0]=false;
a[1]=false;
for(int i=2;i<a.size();i++){
	if(a[i]){
		for(int j=2;j*i<a.size();j++){
			a[i*j]=false;
		}
	}

}
return;
	}

int main(void){
	vector<bool> a(M,true);
	make(a);
	
	while(1){
		int n;
		cin>>n;
		if(n==0)break;
		int up=0,down=0;
		while(1){
			if(a[n+up]){
				break;
			}else{
				up++;
			}
		}
		while(1){
			if(a[n-down]){
				break;
			}else{
				down++;
			}
		}
		cout<<up+down<<endl;
	}
	return 0;
}