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 N 1299710
using namespace std;

int main(){
  int n;
  int p[N];
  
  for(int i=0;i<N;i+=2)p[i] = 0;
  for(int i=1;i<N;i+=2)p[i] = 1;
  p[1] = 0;
  p[2] = 1;

  int c = 3;
  while(c*c<N){
    for(int i=3*c;i<N;i+=2*c)p[i] = 0;
    while(!p[++c]);
  }

  while(1){
    cin >> n;
    if(!n)break;

    if(p[n])cout << 0 << endl;
    else{
      int l,r;
      l = r = n;
      while(!p[--l]);
      while(!p[++r]);
      cout << r - l << endl;
    }
  }
}