#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
using namespace std;
bool f(int a)
{
	if(a<2)return 0;
	for(int i=2;i*i<=a;i++)if(a%i<1)return 0;
	return 1;
}
int n;
int main()
{
	while(cin>>n,n)
	{
		if(n==1)
		{
			cout<<0<<endl;
			continue;
		}
		int r=n,l=n;
		while(!f(r))r--;
		while(!f(l))l++;
		cout<<l-r<<endl;
	}
}

### 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>
#include<vector>
#include<map>
#include<set>
using namespace std;
bool f(int a)
{
	if(a<2)return 0;
	for(int i=2;i*i<=a;i++)if(a%i<1)return 0;
	return 1;
}
int n;
int main()
{
	while(cin>>n,n)
	{
		if(n==1)
		{
			cout<<0<<endl;
			continue;
		}
		int r=n,l=n;
		while(!f(r))r--;
		while(!f(l))l++;
		cout<<l-r<<endl;
	}
}

```