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>
#include <algorithm>
using namespace std;
bool is_prime[1500000];

int main(){
  int n, m = 1500000;
  fill(is_prime,is_prime+m,true);
  vector<int> P;
  for(int i = 2; i*i <= m; ++i){
    if(!is_prime[i]) continue;
    for(int j = i; i*j <= m; ++j){
      is_prime[i*j] = false;
    }
  }
  for(int i = 2; i < m; ++i)
    if(is_prime[i])
      P.push_back(i);
  while(cin >> n, n){
    if(is_prime[n]){
      cout << 0 << endl;
      continue;
    }
    int idx = upper_bound(P.begin(), P.end(), n) - P.begin();
    cout << P[idx] - P[idx-1] << endl;
  }
}

