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<vector>
#define N 1299709

using namespace std;

vector<int> MakePrimeNumber(void);

int main(){
  int i, n, x;
  vector<int> data;

  data = MakePrimeNumber();

  while(1){
    cin >> n;
    if(n == 0) break;

    for(i=0; i<data.size(); ++i){
      if(n == data[i]){
	x = 0;
	break;
      }else if(n < data[i]){
	x = data[i] - data[i-1];
	break;
      }
    }
    cout << x << endl;
  }
  return 0;
}

vector<int> MakePrimeNumber(void){
  int i, j, k;
  vector<int> data;

  data.push_back(2);
  data.push_back(3);
  for(i=5; i<=N; i+=2){
    for(j=1, k=0; data[j]<=sqrt(i); ++j){
      if(i%data[j] == 0){
	k = 1;
	break;
      }
    }
    if(k == 0) data.push_back(i);
  }
  return data;
}