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>
using namespace std;
#define MAX 1000000
#define MAXL 50005
int dp[3][MAXL];

int main(){
	int n;
	static bool c[MAX]={true, true};
	for(int i = 2;i < MAX;i++){
		if(!c[i]){
			for(int j = 2;i*j < MAX;j++)c[i*j] = true;
		}
	}
	dp[0][0] = 1;
	for(int k = 0;k < 2;k++){
		for(int i = 0;i < MAXL;i++){
			if(!c[i]){
				for(int j = 0;j < MAXL - i;j++){
					if(i >= j)dp[k+1][j+i] += dp[k][j];
				}
			}
		}
	}
	//for(int i = 0;i < 30;i++)cout << dp[2][i];
	while(cin >> n, n){
		cout << dp[2][n] << endl;
	}
	return 0;
}