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>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define PRIME_MAX 1500000
vector<bool> prime(PRIME_MAX+1,true);
 
void init_prime(){
	prime[0] = prime[1] = false;
	for(int i=2;i*i<=PRIME_MAX;i++)
		if(prime[i]) for(int j=i*i;j<=PRIME_MAX;j+=i)prime[j] = false;
}

int main(){
	init_prime();
	
	int n;
	while(cin >> n ,n ){
		int h = 0,l = 0;
		for(int i=n;i<prime.size();i++)
			if(prime[i]){h = i;break;}	
		for(int i=n;i>=0;i--)
			if(prime[i]){l = i;break;}
		cout << h - l << endl;
	}
}	