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<string>
#include<cmath>
#include<queue>
#include<map>
#include<set>
#include<list>
#include<iomanip>
#include<vector>
#include<functional>
#include<algorithm>
#include<cstdio>
using namespace std;
bool a[1500000];
int main() {
	fill(a, a + 1500000, true);
	a[0] = false; 1[a] = false;
	for (int i = 2; i < 1500000; i++) {
		if (a[i]) {
			int j = 2;
			while (i*j < 1500000) {
				a[i*j] = false;
				j++;
			}
		}
	}
	int n;
	while (cin >> n&&n != 0) {
		int s = n, e = n;
		while (!a[s]) s--;
		while (!a[e]) e++;
		cout << e - s << endl;
	}
}