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<cstdio>
#include<cmath>
#include<vector>
using namespace std;
#define int long long
const int PMAX=50000;
vector<int> PF(PMAX, 1);
void MKPF(){for (int i=2;i<sqrt(PMAX);i++) if(PF[i]==1) for(int j=i*2;j<PMAX;j+=i) PF[j] = 0;}
signed main(){
	MKPF();
	int a;
	while( scanf("%lld", &a) != EOF ){
		if(a==0) break;
		int c=0;
		for(int i=2; i<=a/2; i++){
			if(PF[i]==1 && PF[a-i]==1) c++;
		}
		cout << c << endl;
	}
	return 0;
}