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
//22
#include<iostream>

using namespace std;

#define MAX 1299709

int main(){
  static bool cmp[MAX+1]={true,true};
  for(int i=2;i<=MAX;i++){
    if(!cmp[i]){
      for(int j=2;j*i<=MAX;j++){
	cmp[i*j]=true;
      }
    }
  }
  for(int n;cin>>n,n;){
    if(!cmp[n]){
      cout<<0<<endl;
    }else{
      int f=n,l=n;
      while(cmp[f]){
	f--;
      }
      while(cmp[l]){
	l++;
      }
      cout<<l-f<<endl;
    }
  }
  return 0;
}