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<cstring>
using namespace std;

#define REP(i,a,b) for(i=a; i<b; ++i)
#define rep(i,n) REP(i,0,n)

int isprime[1299710];

int main() {
  int i,j,k;
  memset(isprime, 0, sizeof(isprime));
  for(i=4; i<1299710; i+=2) isprime[i] = 1;

  for(i=3; i<=1141; i+=2)
    if(isprime[i] == 0)
      for(j=2; i*j<1299710; ++j)
	isprime[i*j] = 1;

  int in;
  while(cin>>in, in) {
    if(isprime[in] == 0) {
      cout<<0<<endl;
      continue;
    }

    int up=0,low=0;
    while(isprime[in+up] == 1) up++;
    while(isprime[in-low] == 1) {
      low++;
    }
    cout<<up+low<<endl;
  }
}