#include <iostream>
#include <algorithm>
using namespace std;
#define N 2000000
bool prime[N+1];
int main(){
  for(int i=2;i<=N;++i) prime[i]=true;
  for(int i=2;i<=N;++i) if(prime[i]) for(int j=2;i*j<=N;++j) prime[i*j]=false;

  int k;
  while(cin>>k,k){
    int m=k,M=k;
    while(!prime[m]) --m;
    while(!prime[M]) ++M;
    cout << M-m << endl;
  }
  return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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

### Response

```cpp
#include <iostream>
#include <algorithm>
using namespace std;
#define N 2000000
bool prime[N+1];
int main(){
  for(int i=2;i<=N;++i) prime[i]=true;
  for(int i=2;i<=N;++i) if(prime[i]) for(int j=2;i*j<=N;++j) prime[i*j]=false;

  int k;
  while(cin>>k,k){
    int m=k,M=k;
    while(!prime[m]) --m;
    while(!prime[M]) ++M;
    cout << M-m << endl;
  }
  return 0;
}
```