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<cmath>
#include<set>
#define MAX 1299710
using namespace std;

bool isPrime[MAX];
set<int> pNum;
void prime(){
  isPrime[0]=isPrime[1]=true;
  for(int i=2;i<MAX;i++){
    if(isPrime[i]==false)pNum.insert(i);
    for(int j=2*i;j<MAX;j+=i)isPrime[j]=true;
  }
}

int main(){
  prime();
  int n;
  while(cin>>n,n){
    int forward,back;
    set<int>::iterator ite;
    ite=pNum.lower_bound(n);
    forward=*ite;
    if(forward!=n && n!=2)ite--;
    back = *ite;
    cout << forward-back << endl;
  }
  return 0;
}