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>
#define X 50000
using namespace std;

int gold(int n,bool p[X+1]){
	if(n%2==1){
		if(p[n-2]) return 1;
		else return 0;
	}
	else{
		int c = 0;
		for(int i=2;i<=X;i++){
			if(n-i<i) break;
			if(p[i] and p[n-i]) c++;
		}
		return c;
	}
}

int main(){
	int n;
	bool p[X+1];
	for(int i=0;i<=X;i++) p[i] = true;
	for(int i=2;i<=X;i++){
		if(not p[i]) continue;
		for(int j=2;j<=X/i;j++) p[i*j] = false;
	}
	while(1){
		cin >> n;
		if(n==0) break;
		cout << gold(n,p) << endl;
	}
}