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 <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
bool s[55555];

void sosuu(int n){
  memset(s,true,sizeof(s));
  s[0] = s[1] = false;
  for(int i = 2; i*i <= n; i++){
    if(!s[i]) continue;
    for(int j = i*2; j <= n; j += i){
      s[j] = false;
    }
  }
}

int main(void)
{
  sosuu(50005);
  while(1){
    int n;
    cin >> n;
    if(!n) break;

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