#include <cstdio>
using namespace std;

bool prime[50010];
int ans[50010];

int main(){
	for(int i = 2; i <= 50000; ++i){
		prime[i] = true;
	}
	for(int i = 2; i < 300; ++i){
		if(prime[i]){
			for(int j = i * i; j <= 50000; j += i){
				prime[j] = false;
			}
		}
	}

	int n;
	while(scanf("%d", &n), n){
		int c = 0;
		for(int i = 2; i * 2 <= n; ++i){
			if(prime[i] && prime[n-i]) ++c;
		}
		printf("%d\n", c);
	}
}
### Prompt

Create a solution in CPP for the following problem:

It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For example, 10 can be represented by the sum of two prime numbers, 7 + 3 and 5 + 5.

Write a program that inputs the integer n and outputs how many combinations of n are the sum of two prime numbers. However, n must be 4 or more and 50,000 or less. Also, the n entered is not always even.



Input

Given multiple datasets. Each dataset is given n on one row. When n is 0, it is the last input. The number of datasets does not exceed 10,000.

Output

For each dataset, output the number of combinations in which n is the sum of two prime numbers on one line.

Example

Input

10
11
0


Output

2
0

### Response

```cpp
#include <cstdio>
using namespace std;

bool prime[50010];
int ans[50010];

int main(){
	for(int i = 2; i <= 50000; ++i){
		prime[i] = true;
	}
	for(int i = 2; i < 300; ++i){
		if(prime[i]){
			for(int j = i * i; j <= 50000; j += i){
				prime[j] = false;
			}
		}
	}

	int n;
	while(scanf("%d", &n), n){
		int c = 0;
		for(int i = 2; i * 2 <= n; ++i){
			if(prime[i] && prime[n-i]) ++c;
		}
		printf("%d\n", c);
	}
}
```