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 <algorithm>
#include <vector>

using namespace std;

const int N = 1299709;

vector<int> prime;
bool is_prime[N + 1];

void sieve(){
  fill(is_prime, is_prime+N+1, true);
  is_prime[0] = is_prime[1] = false;
  for(int i=2;i<=N;i++){
    if(is_prime[i]){
      prime.push_back(i);
      for(int j=2*i;j<=N;j+=i) is_prime[j] = false;
    }
  }
}

int solve(int n){
  if(is_prime[n]) return 0;
  vector<int>::iterator it = upper_bound(prime.begin(), prime.end(), n);
  int r = *it;
  *it--;
  int l = *it;
  return r-l;
}

int main(){
  int n;
  sieve();
  while(cin >> n && n){
    cout << solve(n) << endl;
  }
}