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 <algorithm>
#include <vector>
#include <cmath>
using namespace std;

vector<int> createPrime ( int num )
{
	vector<int> vp;
	vector<bool> vb(num+1, true);
	vb[0] = vb[1] = false;
	for (int i = 2; i <= num; ++i) {
		if (!vb[i]) { continue; }
		vp.push_back(i);
		for (int j = i+i; j <= num; j+=i) { vb[j] = false; }
	}
	return vp;
}

const int MAX = 1299709;

int main() {
	int k;
	vector<int> vp = createPrime(MAX);

	while (cin >> k, k) {
		vector<int>::iterator it = lower_bound(vp.begin(), vp.end(), k);
		if (*it == k || k == 1) {
			cout << 0 << endl;
		}
		else {
			vector<int>::iterator it2 = it - 1;
			cout << *it - *it2 << endl;
		}
	}
	return 0;
}