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>
using namespace std;

string prime(int n){
  int i,j;
  string p="001";
  while(p.size()<=n)p+="10";
  i=3;
  while(i*i<n){
    for(j=3*i;j<n;j+=2*i)p[j]='0';
    do{i+=2;}while(p[i]-'1');
  }
  return p;
}

int main(){
  int n,ans;
  string p = prime(50000);

  while(1){
    cin >> n;
    if(!n)break;

    ans = 0;
    for(int i=0;i<=n/2;i++){
      if(p[i]-'0' && p[n-i]-'0')ans++;
    }
    cout << ans << endl;
  }
}