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>
using namespace std;

vector<bool> pt;

void MakeTable(int n){
  pt.resize(++n);
  pt[0] = pt[1] = false;pt[2] = true;
  
  int i = 2;
  while(++i<n)pt[i] = i&1;
  
  i = 3;
  while(i*i<n){
    for(int j=3*i;j<n;j+=2*i)pt[j]=false;
    do{i+=2;}while(!pt[i]);
  }
}

int main(){
  int n,ans;
  MakeTable(50000);

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

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