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 main()
{
  static const int M = 1299709;
  vector<int> primes;
  vector<bool> sieve(M+1, false);
  sieve[1] = true;
  for (int i = 2; i <= M; i++) {
    if (!sieve[i]) {
      primes.push_back(i);
      for (int j = i+i; j <= M; j += i) {
        sieve[j] = true;
      }
    }
  }

  int k;
  while (cin >> k && k != 0) {
    vector<int>::const_iterator it = lower_bound(primes.begin(), primes.end(), k);
    if (*it == k) {
      cout << 0 << endl;
    } else {
      cout << (*it - *(it-1)) << endl;
    }
  }
  return 0;
}