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>
using namespace std;

#define MAX 1299709+1
int main(){
  int b[MAX]={0},i,j;
  b[0]=b[1]=1;
  for(i=4;i<MAX;i+=2)b[i]=1;
  for(i=3;i*i<MAX;i+=2)
    if(!b[i])for(j=i+i;j<MAX;j+=i)b[j]=1;

  int n,c;

  while(cin>>n,n){
    c=0;
    for(i=n;i>2;i--){
      if(!b[i])break;
      c++;
    }
    for(i=n;i<MAX;i++){
      if(!b[i])break;
      c++;
    }
    if(b[n])cout<<c<<endl;
    else puts("0");
  }
}