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>
using namespace std;

int dt[50001];

int main(){
	dt[0]=0;
	dt[1]=0;
	for(int i=2;i<50001;i++){
		dt[i]=1;
	}
	for(int i=2;i<sqrt(50001);i++){
		for(int j=2;i*j<50001;j++){
			dt[i*j]=0;
		}
	}
	int num=0;
	while(1){
		int cnt=0;
		cin>>num;
		if(num==0)break;
		for(int i=1;i<(num/2+1);i++){
			if(dt[i]==1){
				if(dt[num-i]==1){
					cnt++;
				}
			}
		}
		cout<<cnt<<endl;
	}
	return 0;
}