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 <algorithm>
#include <vector>
using namespace std;

const int C = 1300000;
bool isprime[C];
vector<int> prime;

void init() {
  fill(isprime, isprime+C, true);
  isprime[0] = isprime[1] = false;
  for (auto i=2; i<C; i++) {
    if (isprime[i]) {
      prime.push_back(i);
      for (auto j=2; j<C; j++) {
	if ( i * j >= C) break;
	isprime[i*j] = false;
      }
    }
  }
}

int main() {
  init();
  int N;
  while (cin >> N && N) {
    if (isprime[N]) {
      cout << "0" << endl;
    } else {
      int p = 0;
      int q = 0;
      for (auto i=0; i<prime.size(); i++) {
	if (prime[i] < N) p = prime[i];
	else if (prime[i] > N) {
	  q = prime[i];
	  break;
	}
      }
      cout << q-p << endl;
    }
  }
}