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>
#include <cmath>
using namespace std;

#define N 1299709

int main(void){
	vector<bool> isprime(N+1);
	for(int i=0;i<isprime.size();i++) isprime[i]=true;
	int upto = (int)sqrt(isprime.size());
	isprime[1]=false;
	for(int i=2;i<=upto;++i){
		if(isprime[i]){//消されてなければその倍数を消す
			for(int j=2;i*j<isprime.size();++j) isprime[i*j] = false;
		}
	}
	int n;
	while(cin>>n,n){
		int min=2,max=N;
		for(int i=0;n-i>1;++i) if(isprime[n-i]){min=n-i;break;}
		for(int i=0;n+i<=N;++i) if(isprime[n+i]){max=n+i;break;}
		cout<<max-min<<endl;
	}
	return 0;
}