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 <bits/stdc++.h>
using namespace std;

vector<int> p;

void solve(int n){
	auto ub = upper_bound(p.begin(), p.end(), n);
	auto lb = lower_bound(p.begin(), p.end(), n);
	if(ub != lb) cout << 0 << "\n";
	else cout << *ub - *(ub-1) << "\n";
}

int main(){
//	cin.tie(0);
//	ios::sync_with_stdio(false);
	for(int i=2; i<=1299709; ++i){
		bool f = true;
		for(int j=0; j<p.size()&&p[j]*p[j]<=i; ++j)
			if(i % p[j] == 0){
				f = false;
				break;
			}
		if(f) p.push_back(i);
	}
	while(1){
		int n;
		cin >> n;
		if(n == 0) return 0;
		solve(n);
	}
}
