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<algorithm>
#include<iostream>
#include<string>
#include<cstdlib>
#include<cstring>
#include<cmath>
using namespace std;
int main(){
  int i,j,k,l;
  int a[100000];
  a[0]=2;
  k=1;
  for(i=3;k<100000;i+=2){
    l=(int)sqrt(i)+1;
    for(j=3;j<l;j+=2){
      if(i%j==0)
	break;
    }
    if(j>=l){
      a[k]=i;
      k++;
    }
  }
  int n;
  while(cin>>n&&n){
    for(i=0;a[i]<n;i++);
    if(a[i]==n)
      cout<<0<<endl;
    else
      cout<<a[i]-a[i-1]<<endl;
  }
  return 0;
}