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 <cstring>
using namespace std;

bool primeFlg[1000000];

void makePrime(){
  memset(primeFlg, true, sizeof(primeFlg));
  primeFlg[0] = primeFlg[1] = false;
 
  for(int i = 2; i * i <= 1000000; i++){
    if(primeFlg[i]){
      for(int j = i + i; j < 1000000; j += i){
        primeFlg[j] = false;
      }
    }
  }
}

int main(){
  makePrime();

  int n;

  while(cin >> n, n){
    int answer = 0;

    for(int i = 2; i < n; i++){
      int j = n - i;

      if(i <= j && primeFlg[i] && primeFlg[j]){
        answer++;
      }
    }

    cout << answer << endl;
  }
}