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>
using namespace std;

bool f[1300001] = {};
long long int len[1300001] = {};

int main() {

  long long int k = 0;

  for ( long long int i = 2; i < 1300000; i++ ) {

    if ( f[i] == false ) {

      len[k] = i - k;
      for ( long long int j = 2; j * i < 1300000; j++ ) {
	f[j*i] = true;
      }
      k = i;

    }else {

      len[i] = k;

    }

  }

  while( true ) {

    long long int n;
    cin >> n;
    if ( n == 0 ) break;

    if ( f[n] == false ) {
      cout << 0 << endl;
    }else {
      cout << len[len[n]] << endl;
    }

  }

  return 0;

}