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 STA 50000
using namespace std;

int prime[50001];

int main(){
  int n;
  int cnt;
  for(int i=2;i<=STA/2;i++){
    for(int j=2;i*j<=STA;j++){
      prime[i*j] = 1;
    }
  }
  while(1){
    cnt = 0;
    cin >> n;
    if(n == 0) break;
    for(int i=2;i<=n/2;i++){
	if(prime[i] == 0 && prime[n-i] == 0) cnt++;
    }
    cout << cnt << endl;
  }
}