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>
using namespace std;
using ll = long long;
const int MOD = 1e9 + 7;

bool prime[2000000] = {};
void Eratosthenes(int n)
{
  for (int i = 2; i <= (int)sqrt(n) + 1; ++i)
  {
    if (prime[i] == 0)
    {
      for (int j = i * 2; j <= n; j += i)
      {
        prime[j] = 1;
      }
    }
  }
}

int main()
{
  Eratosthenes(1299709);
  int k;
  vector<int> ans;
  while (cin >> k, k)
  {
    int cnt = 0;
    int pk = k, nk = k;
    while (prime[pk] && pk < 1299709)
    {
      cnt++;
      pk++;
    }
    while (prime[nk] && nk > 1)
    {
      cnt++;
      nk--;
    }
    ans.push_back(cnt);
  }
  for (auto &e : ans)
    cout << e << endl;

  return 0;
}

