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 <bits/stdc++.h>
#define REP(i, a, n) for(ll i = ((ll) a); i < ((ll) n); i++)
using namespace std;
typedef long long ll;

const ll MAX = 1299709;

int main(void) {
  vector<bool> isp(MAX + 1, true);
  isp[0] = isp[1] = false;
  REP(i, 0, MAX + 1) if(isp[i]) for(ll j = i + i; j <= MAX; j += i) isp[j] = false;
  vector<ll> prime;
  REP(i, 0, MAX + 1) if(isp[i]) prime.push_back(i);

  ll N;
  while(cin >> N, N) {
    if(binary_search(prime.begin(), prime.end(), N)) {
      cout << 0 << endl;
    } else {
      auto t = lower_bound(prime.begin(), prime.end(), N);
      cout << (*t - *(t - 1)) << endl;
    }
  }
}

