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 <set>
using namespace std;
bool p[50000];
int main()
{
  int i,j;
  set<int> s;
  for(i=2;i<50000;i++){
    if(!p[i]){
      s.insert(i);
      for(j=i*2;j<50000;j+=i){
	p[j] = true;
      }
    }
  }
  while(cin >> i,i){
    int c = 0;
    set<int>::iterator it = s.begin();
    while(it != s.end() && (*it) <= i / 2){
      if(s.find(i - *it) != s.end()) {
	c++;
      }
      it++;
    }
    cout << c << endl;
  }
  return 0;
}