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 <cstdio>
#include <cstring>
using namespace std;
int main(){
	int n;
	bool f[50010];
	memset(f,true,sizeof(f));
	f[1]=false;f[0]=false;
	for(int i=2;i<300;i++){
		if(f[i]){
			for(int j=i*i;j<50001;j+=i)f[j]=false;
		}
	}
	while(cin>>n,n){
		int ans=0;
		for(int i=2;i<=n/2;i++){
			if(f[i]&&f[n-i])ans++;
		}
		cout<<ans<<endl;
	}
}