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 <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define N 100000

int primes[N+10];
void li(){
	int p=0,i,j;bool b;
	primes[p++]=2;
	for(i=3;;i+=2){
		b=true;
		for(j=0;j<p&&primes[j]*primes[j]<=i;j++){
			if(i%primes[j]==0) {b=false;break;}
		}
		if(b) primes[p++]=i;
		if(p==N) break; 
	}
	//cout<<primes[N-1]<<endl;
}
int main(){
	li();
	int n;
	while(scanf("%d",&n)&&n){
		int z=lower_bound(primes,primes+N,n)-primes;
		if(primes[z]==n) puts("0");
		else{
			printf("%d\n",primes[z]-primes[z-1]);
		}
	}
	
	return 0;
}
