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>
#define Number 1299710
using namespace std;

int table[Number]={0,0};

int main(){
  int n;
  for(int i=2;i<Number;i++)
    table[i]=1;
  for(int i=2;i<Number;i++){
    if(table[i]){
      for(int j=i+i;j<Number;j+=i){
	table[j]=0;
      }
    }
  }
  while(cin>>n,n){
    if(table[n]){
      cout<<0<<endl;
    }else{
      int lower=n;
      int higher=n;
      while(!table[--lower])
	;
      while(!table[++higher])
	;
      cout<<higher-lower<<endl;

    }

  }
  return 0;
}