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<vector>
#include<cmath>
using namespace std;
int main(){
  short ans[50001]={};
  vector<int>pri;
  pri.push_back(2);
  for(int i=3;i<=50000;i+=2){
    int flag=1;
    for(int j=2;j<=sqrt(i);j++){
      if(i%j==0){
	flag=0;
	break;
      }
    }
    if(flag)
      pri.push_back(i);
  }
  for(int i=0;i<pri.size();i++){
    for(int j=i;j<pri.size();j++){
      if(pri[i]+pri[j]>50000)
	break;
      ans[pri[i]+pri[j]]++;
    }
  }
  int n;
  while(cin>>n,n)
    cout<<ans[n]<<endl;
  return 0;
}