#include <bits/stdc++.h>

using namespace std;

bool isPrime(int n){
	for(int i=2;i<=sqrt(n);i++){
		if(n%i==0) return false;
	}
	return true;
}

int main(){
	int n;
	while(cin >> n,n){
		int x=n,y=n;
		while(!isPrime(x)) x++;
		while(!isPrime(y)) y--;
		cout << x-y << endl;
	}
	
	return 0;
}
### Prompt

Your task is to create a cpp solution to the following problem:

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 <bits/stdc++.h>

using namespace std;

bool isPrime(int n){
	for(int i=2;i<=sqrt(n);i++){
		if(n%i==0) return false;
	}
	return true;
}

int main(){
	int n;
	while(cin >> n,n){
		int x=n,y=n;
		while(!isPrime(x)) x++;
		while(!isPrime(y)) y--;
		cout << x-y << endl;
	}
	
	return 0;
}
```