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 <vector>
#include <iostream>
#include <algorithm>
using namespace std;
vector<int> P;
const int pmax=1299709;
bool iscomp[pmax+1];
void init()
{
	P.reserve(100000);
	for(int i=2;i<pmax+1;i++){
		if(iscomp[i])continue;
		P.push_back(i);
		for(int j=2;i*j<pmax+1;j++)
			iscomp[i*j]=true;
	}
}
int main()
{
	init();
	while(true){
		int n;
		cin>>n;
		if(n==0)return 0;
		int pos=lower_bound(P.begin(),P.end(),n)-P.begin();
		if(P[pos]==n)cout<<0<<endl;
		else{
			cout<<P[pos]-P[pos-1]<<endl;
		}
	}
}