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>
#define N 50000
using namespace std;
int main(){
  int n;
  int p[N]={0};
  for(int i=3;i<=N;i+=2) p[i] = 1;
  p[2] = 1;
  for(int i=3;i<=1000;i+=2){
    if(p[i]==1){
      for(int j=2*i;j<=N;j+=i) p[j] = 0;
    }
  }
  while(cin >> n){
    if(n==0) break;
    int count = 0;
    for(int i=2;i<=n/2;i++){
      if(p[i]==1&&p[n-i]==1) count++;
    }
    cout << count << endl;
  }
  return 0;
}