#include<stdio.h>
int P(int x)
{
	if(x==2)return 1;
	if(x%2==0)return 0;
	for(int i=3;i*i<=x;i+=2)if(x%i==0)return 0;
	return 1;
}
int main()
{
	int r,n,i;
	while(scanf("%d",&n),n)
	{
		if(P(n))puts("0");
		else
		{
			r=2;
			for(i=1;!P(n+i);++i)++r;
			for(i=1;!P(n-i);++i)++r;
			printf("%d\n",r);
		}
	}
	return 0;
}
### Prompt

Please formulate 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<stdio.h>
int P(int x)
{
	if(x==2)return 1;
	if(x%2==0)return 0;
	for(int i=3;i*i<=x;i+=2)if(x%i==0)return 0;
	return 1;
}
int main()
{
	int r,n,i;
	while(scanf("%d",&n),n)
	{
		if(P(n))puts("0");
		else
		{
			r=2;
			for(i=1;!P(n+i);++i)++r;
			for(i=1;!P(n-i);++i)++r;
			printf("%d\n",r);
		}
	}
	return 0;
}
```