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<cstdio>
#include<cstdlib>
#include<vector>
#include<string>
#include<sstream>
#include<cmath>
#include<numeric>
#include<map>
#include<stack>
#include<queue>
#include<list>
using namespace std;
int inf = 1000000000;

vector<bool> isPrime(int n){
  vector<bool> p(n+1, true);
  p[0] = false;
  p[1] = false;
  for(int i=2; i<=sqrt(n); i++){
    if( !p[i] ) continue;
    for(int j=i+i; j<=n; j+=i) p[j] = false;
  }
  return p;
}

int main(void) {
  vector<bool> p = isPrime(10000000);
  int n;
  while(cin >> n){
    if( n == 0 ) break;
    int l = n, r = n;
    while( !p[l] ) l--;
    while( !p[r] ) r++;
    cout << r - l << endl;
  }

  return 0;
}

// EOF