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>
using namespace std;
#define MAX 1299710
int main (){
	bool pr[MAX];
	int a;
	vector <int> prl;
	for(int i=0;i<MAX;i++) pr[i]=true;
	pr[0]=false;
	pr[1]=false;
	
	for(int i=0;i*i<MAX;i++){
		if(pr[i]){
			for(int j=i*i;j<=MAX;j=j+i){
				pr[j]=false;
			}
		}
	}
	for(int i=0,j=0;i<100000;j++){
	    if(pr[j]==true){
	        prl.push_back(j);
	        i++;
	    }
	}
	while(cin>>a){
		if(a==0)break;
		if(pr[a]){
		    cout << 0 <<endl;
		}
		else{
		    auto ansitr=lower_bound(prl.begin(),prl.end(),a);
		    cout<< *ansitr - *(ansitr-1) <<endl;
		}
	}
}