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>

using namespace std;

#define N 1299710

int main(int argc, char const *argv[])
{
	int n;
	int p1,p2;

	bool f[N];

	for(int i1=0;i1<N;i1++) f[i1]=false;

	f[0]=true;
	f[1]=true;
	for(int i1=0;i1<N;i1++){
		if(f[i1]==false){
			for(int i2=2;i2*i1<N;i2++){
				f[i2*i1]=true;
			}
		}
	}

	while(1){
		cin>>n;
		if(n==0) break;

		p1=n;
		while(f[p1]==true) p1--;
		p2=n;
		while(f[p2]==true) p2++;

		cout<<p2-p1<<endl;

	}
	return 0;
}