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;

int k;
vector<int> pvec;
bool prime[1500005];

int main(void)
{
  for(int i = 2; i < 50005; i++){
    if(prime[i]) continue;
    for(int j = 2*i; j < 1500005; j+=i) prime[j] = true;
  }
  for(int i = 2; i < 1500005; i++){
    if(!prime[i]) pvec.push_back(i);
  }

  while(1){
    cin >> k;
    if(k == 0) break;
    int u = *lower_bound(pvec.begin(), pvec.end(), k);
    if(u == k){
      cout << 0 << endl;
      continue;
    }
    int l = *(lower_bound(pvec.begin(), pvec.end(), k) - 1);
    cout << u - l << endl;
  }
  return 0;
}

