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
#include <cstdio>
#include <vector>
using namespace std;

bool isprime[50010];
int ans[50010];

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

	vector<int> primes;
	for(int i = 2; i <= 50000; ++i){
		if(isprime[i]) primes.push_back(i);
	}

	for(int i = 0; primes[i] <= 25000; ++i){
		for(int j = i; primes[i] + primes[j] <= 50000; ++j){
			++ans[primes[i] + primes[j]];
		}
	}

	int n;
	while(scanf("%d", &n), n){
		printf("%d\n", ans[n]);
	}
}