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 <cstring>
using namespace std;

#define MAXN 1299710

bool p[MAXN];

int main() {

int i, j, N;

memset(p, true, sizeof(p));;
for (i=2; i<MAXN; i++) {
   if (p[i] == true) {
		for (j=2*i; j<MAXN; j+=i) {
			p[j] = false;
		}
	}
}

cin >> N;

do {

i = N; while (p[i] == false) i++;
j = N; while (p[j] == false) j--;

cout << i-j << endl;

cin >> N;

} while (N!=0);

return 0;
}