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>
#define MAX 100000
using namespace std;
int main(){
    vector<bool> v(MAX);
    for(int i = 0;i<MAX;i++)
      v[i]=true;

      v[0]=v[1]=false;
    for(int i = 2;i<1000;i++){
      if(v[i]){
        for(int j=i*i;j<MAX;j+=i){
         v[j]=false;
       }
      }
    }
    while(true){
      int a;
      int ans =0;
      cin >> a;
      if(a==0)return 0;
      for(int i = 2;i<=a/2;i++){
        if(v[a-i]&&(v[i]))ans++;
      }
      cout <<ans<<endl;
    }
}

