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 <bits/stdc++.h>
using namespace std;

const int MAXN = 50001;

bool prime[MAXN] = {true, true};

int main()
{
  for (int i = 2; i * i < MAXN; i++){
    for (int j = i * i; j < MAXN; j += i){
      prime[j] = true;
    }
  }
  
  int n;
  while (scanf("%d", &n), n){
    int cnt = 0;
    for (int i = 2; i <= n / 2; i++){
      if (!prime[i] && !prime[n - i]){ // i + (n - i) = n
        cnt++;
      }
    }
    printf("%d\n", cnt);
  }

  return (0);
}