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 <cmath>
using namespace std;

int p[100010], size;

bool isPrime(int x){
	for(int i=0;i<size && p[i]<=sqrt(x);i++){
		if(x % p[i] == 0) return false;
	}
	return true;
}

int main(void){
	int n;

	p[0] = 2;
	size = 1;
	for(int i=3;i<1299730;i+=2) if(isPrime(i)) p[size++] = i;

	while(cin>>n && n){
		int i;
		for(i=0;p[i]<n;i++);

		if(p[i] == n) cout<<"0\n";
		else cout<<p[i] - p[i-1]<<endl;
	}

	return 0;
}