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<string.h>
 
using namespace std;
 
bool p[50001];
int  cnt;
int  n;
 
void prime()
{
 
  for(int i = 2; i*i <= 50000; i++){
    if(!p[i]){
      for(int j = i*i; j <= 50000; j+=i){
        p[j] = true;
      }
    }
  }
  p[0] = p[1] = true;
}
 
int main(void)
{
 
  prime();
 
  while(cin >> n && n){
    cnt = 0;
    for(int i = 2; i <= n/2; i++){
      if(!p[i] && !p[n-i]){
        cnt++;
      }
    }
    cout << cnt << endl;
  }
 
  return 0;
}