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>
#define rep(i, n) for(int i = 0; i < (n); i++)
using namespace std;
bool prime[1300000] = {0};

int main(){
  prime[0] = prime[1] = 1;
  rep(i, 1300000){
    if(prime[i])continue;
    for(int j = i+i; j < 1300000; j+=i)prime[j]=1;
  }
  int n;
  while(cin>>n, n){
    if(!prime[n]){
      cout<<0<<endl;
      continue;
    }
    int mx, mn;
    for(mx = n; prime[mx]; mx++);
    for(mn = n; prime[mn]; mn--);
    cout<<mx-mn<<endl;
  }
  return 0;
}