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>
using namespace std;

vector<bool> Eratos(1299710,true);

int main()
{
	int N,min,max;
	for (int i = 2; i < 1142;) {
		for (int j = i * 2; j <= 1299710; j += i) {
			if (j % i == 0) {
				Eratos[j] = false;
			}
		}
		for (i++;!Eratos[i];i++);
	}
	while (cin >> N, N) {
		for (min = N; !Eratos[min]; min--);
		for (max = N; !Eratos[max]; max++);
		cout << max - min << endl;
	}
	return 0;
}