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<vector>
#include<cstdio>
#include<algorithm>
#define MAX 50010
using namespace std;
int main(){
	int sum,k=0;
	vector<int> pri(MAX);
	vector<int> pre(MAX);
	for(int i=0;i<MAX;i++)
	pri[i]=1;
	pri[0]=0;
	pri[1]=0;
	for(int i=0;i*i<MAX;i++){
		if(pri[i]){
			for(int j=i*2;j<MAX;j+=i){
				pri[j]=0;
			}
		}
	}
	for(int i=0;i<MAX;i++)
	if(pri[i]){
	pre[k++]=i;
	}
	int n;
	while(cin>>n,n){
		sum=0;
		for(int i=0;pre[i]<=n/2;i++){
			if(pri[n-pre[i]])
				sum++;
		}
		cout<<sum<<endl;
	}
	return 0;
}