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>

#define LIM 2000000

using namespace std;

int main(){

	bool nprime[LIM]={0};
	
	for(int i=2; i<LIM; ++i){
		
		if(!nprime[i]){
			for(int j=i+i; j<LIM; j+=i){
				nprime[j]=true;
			}
		}
	}
	
	vector<int> p;
	
	for(int i=2; i<LIM; ++i){
		if(!nprime[i]){
			p.push_back(i);
		}
	}
	
	int k;
	
	while(cin >> k, k){
		
		vector<int>::iterator it = lower_bound(p.begin(), p.end(), k);
		
		if(*it==k)
			cout << 0 << endl;
		else
			cout << *it - *(it-1) << endl;
	}
	
	return 0;
}
	