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 <iostream>
#include <math.h>

#define N 50001

using namespace std;

int main(void){
	bool isprime[N];
	for(int i=0;i<N;i++) isprime[i]=true;
	int upto = (int)sqrt(N);
	for(int i=2;i<=upto;i++){
		if(isprime[i]){//消されてなければその倍数を消す
			for(int j=2;i*j<=N;j++) isprime[i*j] = false;
		}
	}
	int n;
	while(cin >> n){
		if(n==0)break;
		int count=0;
		for(int i=2;i<=n/2;i++){
			if(isprime[n-i]&&isprime[i])count++;
		}
		cout<<count<<"\n";
	}
	return 0;
}