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<vector>
#include<cmath>
#include<algorithm>

using namespace std;

const int MAX = 1299710;
bool prime[MAX];
vector<int> V;

void make(){
  fill(prime,prime+MAX, 1);
  prime[0] = prime[1] = 0;
  for(int i = 2; i < sqrt(MAX); i++)
    if(prime[i]) for(int j = 2*i; j < MAX; j+=i) prime[j] = 0;

  for(int i = 2; i < MAX; i++) 
    if(prime[i]) V.push_back(i);
}
int main(){
  make();
  vector<int>::iterator ite;
  int in;
  while(cin >> in && in){
    ite = upper_bound(V.begin(),V.end(),in);
    if(!prime[in])cout << *ite-*(ite-1) << endl;
    else cout << "0" << endl;
  }
  return 0;
}