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;

bool is_prime[1500100];
vector<int> primes;

void calc_prime(int n){
	for(int i = 0; i <= n; ++i)
		is_prime[i] = true;
	is_prime[0] = is_prime[1] = false;
	for(int i = 2; i <= n; ++i){
		if(is_prime[i]){
			primes.push_back(i);
			for(int j = i * 2; j <= n; j += i)
				is_prime[j] = false;
		}
	}
	return;
}

int main() {
	calc_prime(1300000);
	int n;
	while(cin >> n && n){
		auto it = lower_bound(primes.begin(), primes.end(), n);
		if(*it == n){
			cout << "0" << endl;
		}
		else{
			cout << *it - *(it - 1) << endl;
		}
	}
	return 0;
}