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 <cstring>
using namespace std;
int main(){
  bool p[50001];
  memset(p, 1, sizeof(p));
  p[0] = p[1] = 0;
  for(int i = 0 ; i < 50001 ; i++){
    if(p[i]){
      for(int j = 2 * i ; j < 50001 ; j += i){
	p[j] = 0;
      }
    }
  }

  int n, sum;
  while(cin >> n, n){
    int cnt = 0;
    for(int i = 0 ; i <= n / 2 ; i++){
	if(p[i] == 1 && p[n - i] == 1) cnt++; 
    }
    cout << cnt << endl;
  }
  return 0;
}