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;

int main()
{
  bool pri[1300000];
  //  vector<int> price;
  fill(pri,pri+1300000,true);
  pri[0]=pri[1]=false;
  for(int i=2;i<1300000;i++)
    {
      if(pri[i]==0)
	continue;
      //  price.push_back(i);	
      for(int j=i+i;j<1300000;j+=i)
	{
	  pri[j]=false;
	}
    }
  int n;
  for(;cin>>n,n;)
    { 
      
      if(pri[n])
	cout<<"0"<<endl;
      else
	{
	  int max,min;
	  for(int i=n-1;;i--)
	    {
	      if(pri[i])
		{
		  min=i;
		  break;
		}
	    }
	  for(int i=n+1;;i++)
	    {
	      if(pri[i])
		{
		  max=i;
		  break;
		}
	    }
	  cout<<max-min<<endl;
	}    
    }
 
}