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 <algorithm>
#include <string>
using namespace std;

const int MAX = 10001000;
bool IsPrime[MAX];
vector<int> Era(int n = MAX) {
    vector<int> res;
	IsPrime[0] = false; IsPrime[1] = false; 
	for (int i = 2; i < n; ++i) IsPrime[i] = true;
	for (int i = 2; i < n; ++i) {
		if (IsPrime[i]) {
            res.push_back(i);
			for (int j = i*2; j < n; j += i) IsPrime[j] = false;
		}
	}
    return res;
}

int main() {
  Era();
  long long N;
  while (cin >> N) {
	if (N == 0) break;
	int prev = N, next = N;
	while (!IsPrime[prev]) --prev;
	while (!IsPrime[next]) ++next;
	cout << next - prev << endl;
  }
}

