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<algorithm>
using namespace std;

#define MAXP 1299709
bool prime[MAXP+1];
void init(){
	prime[2]=true;
	for(int i=3;i<=MAXP;i++)prime[i]=true;
	for(int i=3;i<=MAXP;i++){
		if(!prime[i])continue;
		for(int j=2*i;j<=MAXP;j+=i)prime[j]=false;
	}
}

int main(){
	int n;
	init();
	while(cin>>n&&n){
		int low=n,high=n;
		while(!prime[low])low--;
		while(!prime[high])high++;
		cout<<high-low<<endl;
	}
	return 0;
}