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<algorithm>
#define MAX 1299709
using namespace std;
int main()
{
	int gaps[MAX+1];
	bool used[MAX+1];
	fill(gaps,gaps+MAX+1,0);
	fill(used,used+MAX+1,0);
	int pos=0;
	for(int i = 2; i <= MAX; ++i)
	{
		if(used[i]) continue;
		gaps[pos++]=i;
		for(int j = i*2; j <= MAX; j+=i)
		{
			used[j]=true;
		}
	}

	int k;
	while(cin>>k,k) 
	{
		for(int i = 1; i < pos; ++i)
		{
			if(gaps[i-1]==k||gaps[i]==k)
			{
				cout<<0<<endl;
				break;
			}
			else if(gaps[i-1]<k&&k<gaps[i])
			{
				cout<<gaps[i]-gaps[i-1]<<endl;
				break;
			}
		}
	}
  return 0;
}