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<cmath>
#define N 1299710
using namespace std;

int main(){
  int pn[N]={},n,f,st,end,fst;
  pn[0]=1,pn[1]=1;
  for(int i=2;i<sqrt(N);i++)
    for(int j=2;j*i<N;j++)
      if(pn[i]==0) pn[i*j]=1;
  while(1){
  cin>>n;
  if(n==0) break;
  st=0,end=0,f=0,fst=0;
  while(1){
    if(f==1 || pn[n]==0) break;
    st=0,end=0;
    for(int i=fst;i<N;i++){
           if(i==n) f=1;
      if(pn[i]==0 && st==0) st=i;
      if(pn[i]==0 && st!=i) end=i;
        if(st>0 && end>0){
	fst=end;
	break;
      }
    }
  }
     cout<<end-st<<endl;      
  }
  return 0;
}