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>
using namespace std;
int main() {
  int M = 1299710, n, l, r;
  vector<bool> P(M, true);
  for (int i = 2; i*i < M; ++i) {
    if (P[i]) {
      for (int j = i; i*j < M; ++j) {
	P[i*j] = false;
      }
    }
  }
  while (cin >> n, n) {
    r = n;
    l = n;
    while (!P[r]) ++r;
    while (!P[l]) --l;
    cout << r - l << endl;
  }
  return 0;
}