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<bits/stdc++.h>
using namespace std;
int prime(int x) {
	if (x < 2)return 0;
	else if (x == 2) return 1;
	if (x % 2 == 0) return 0;
	for (int i = 3; i*i <= x; i += 2) {
		if (x%i == 0) return 0;
	}
	return 1;
}
int main(){
	int n;
	while (cin >> n, n) {
		if (prime(n))cout << 0 << endl;
		else { 
			int x = n, y = n;
			while (!prime(x)) {
				x--;
			}
			while (!prime(y)) {
				y++;
			}
			cout << y - x << endl;
		}
	}
}


