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
//Prime Gap
#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

vector<ll> prime;

int main(){
  prime.push_back(2);
  for(ll i=3; i<1300000; i+=2){
    bool flag=true;
    for(ll j=0; j<prime.size() && i>=prime[j]*prime[j]; j++){
      if(i%prime[j]==0){flag=false; break;}
    }
    if(flag)prime.push_back(i);
  }
  while(true){
    int n;
    cin>>n;
    if(n==0)break;
    ll to;
    for(to=0; n>prime[to]; to++);
    if(n==prime[to])cout<<"0"<<endl;
    else cout<<prime[to]-prime[to-1]<<endl;
  }
  return 0;
}