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 <algorithm>
#include <vector>
#include <utility>
#include <cstring>
using namespace std;

#define rep(i,n) for(int i=0; i<n; i++)
typedef long long ll;

const int MAX = 1300000;
bool prime[MAX];

int main() {
	prime[0] = prime[1] = true;
	for(int i=2; i*i<MAX; i++) {
		if(!prime[i]) {
			for(int j=i+i; j<MAX; j+=i) {
				prime[j] = true;
			}
		}
	}
	vector<int> primes;
	for(int i=2; i<MAX; i++) {
		if(!prime[i])
			primes.push_back(i);
	}

	int n;
	while(cin >> n, n) {
		int l = 0;
		while(primes[l+1]<n) l++;
		if(n==2 || n == primes[l+1]) cout << 0 << endl;
		else cout << primes[l+1]-primes[l] << endl;
	}
	return 0;
}