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;
typedef long long ll;
#define MAX 50004
int dp[MAX], d[MAX];

int main(){
	int n, m = 0;
	static bool c[MAX]={true, true};
	for(ll i = 2;i < MAX;i++){
		if(!c[i]){
			for(ll j = 2;i*j < MAX;j++)c[i*j] = true;
			d[m++] = i;
		}
	}
	
	for(int i = 0;i < 3000;i++)
		for(int j = i;d[i]+d[j] < MAX-3;j++)
			dp[d[i] + d[j]]++;
	while(cin >> n, n)cout << dp[n] << endl;
	return 0;
}