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 <stdio.h>
using namespace std;

int f[50001],pr[5500];

int main() {
	int i,j,n=0,cn;
	for (i=2;i<50001;i++) if (f[i]==0) { f[i]=1; pr[n++]=i; for (j=i+i;j<50001;j+=i) f[j]=2;}
	while(cin >> n) {
		if (n==0) break;
		cn=0;
		for (i=0;n/2>=pr[i];i++) if (f[n-pr[i]]==1) cn++;
		cout << cn << endl;
	}
	return 0;
}