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>

using namespace std;

bool is_prime(int n){
	if(n<=1)return false;
	for(int i=2;i*i<=n;i++){
		if(n%i==0)return false;
	}
	return true;
}

int main(){
	int n;
	while(cin>>n && n){
		if(is_prime(n)){
			cout<<0<<endl;
			continue;
		}
		else{
			int ans=1;
			for(int i=n+1;!is_prime(i);i++)ans++;
			for(int i=n-1;!is_prime(i);i--)ans++;
			cout<<ans+1<<endl;
		}
	}
}