#include <iostream>
#include <vector>

using namespace std;

int main()
{
	vector<int> isp(1299710,1);
	isp[0]=isp[1]=0;
	for(int i=2;i*i<isp.size();i++)
		for(int j=i*i;j<isp.size();j+=i)
			isp[j]=0;
	
	for(int k;cin>>k,k;){
		int i,j;
		for(i=k;!isp[i];i--);
		for(j=k;!isp[j];j++);
		cout<<j-i<<endl;
	}
	
	return 0;
}
### Prompt

Please provide a Cpp coded solution 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 <vector>

using namespace std;

int main()
{
	vector<int> isp(1299710,1);
	isp[0]=isp[1]=0;
	for(int i=2;i*i<isp.size();i++)
		for(int j=i*i;j<isp.size();j+=i)
			isp[j]=0;
	
	for(int k;cin>>k,k;){
		int i,j;
		for(i=k;!isp[i];i--);
		for(j=k;!isp[j];j++);
		cout<<j-i<<endl;
	}
	
	return 0;
}
```