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;
 
const int MAX= 10000100;
bool prime[MAX];
void make_prime(){
  for(int i = 0 ; i < MAX ; i ++) prime[i]=true;
  prime[0]=prime[1]=false;
  for(int i = 0; i < MAX; i ++)
    if(prime[i]){
      for(int j = i * 2 ; j < MAX ; j += i)
	prime[j]=false;
    }
}
 
int main(void){
  make_prime();
  long long int n;
  while(cin>>n,n){
    if(prime[n]){
      cout<<0<<endl;
      continue;
    }
    long long int k,j;
    
    for(k = n; !prime[k]; k--);
    for(j = n; !prime[j]; j++);
    cout<<j-k<<endl;
    
  }
}