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 <vector>
using namespace std;
const int MAX = 1299710;
int prime[MAX];

int cal(int n){
  int l = 0;
  int f = 0;
  for(l = n;!prime[l];l++){
  }
  for(f = n;!prime[f];f--){
  }
  return l - f;
  
}
int main(){
  prime[1] = 0;
  prime[2] = 1;
  fill(prime,prime+MAX,1);
  for(int i = 2;i < MAX;i++){
    if(prime[i]){
      for(int j = i+i;j < MAX;j+=i){
	prime[j] = 0;
      }
    }
  }
  /*  for(int i = 1;i < 100;i++){
    if(prime[i])cout << i << endl;
    }*/
  int n;
  while(cin >> n,n != 0){
    cout << cal(n) << endl;
  }

  return 0;
}