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 <cstdio>
#include <iostream>
using namespace std;

const long N=1500000;

int main(){
	bool prime[N];
	
	for(long i=2; i<N; ++i) prime[i]=true;
	
	for(long i=2; i<N; ++i){
		if(prime[i])
			for(long j=2; i*j<N; ++j) prime[i*j]=false;
	}	
	
	while(1){
		long n;
		scanf(" %ld", &n);
		if(n==0) break;
		
		long a, b;
		for(long i=n; i<N; ++i){
			if(prime[i]){
				a=i;	
				break;
			}
		}
		for(long i=n; i>0; --i){
			if(prime[i]){
				b=i;	
				break;
			}
		}
		//printf("%ld-%ld=",a, b);
		printf("%ld\n", a-b);
	}
	return 0;
}