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<cmath>
#define loop(i,a,b) for(int i=a;i<b;i++)
#define rep(i,a) loop(i,0,a)
using namespace std;

int main(){
	bool prime[50001];
	rep(i,50001)prime[i]=true;
	prime[0]=prime[1]=false;
	for(int i=2;i<50001;i++){
		for(int j=i*2;j<50001;j+=i){
			prime[j]=false;
		}
	}
	int n;
	int cnt=0;
	while(cin>>n,n){
		cnt=0;
		for(int i=1;i<=n/2;i++){
			if(prime[i] && prime[n-i])cnt++;
		}
		cout<<cnt<<endl;
	}
	return 0;
}