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<cmath>
using namespace std;

#define M 50010

int main() {
  bool p[M];
  int sqM = (int)sqrt(M), n;
  for(int i=0; i<M; ++i) p[i] = true;
  p[0] = p[1] = false;
  for(int i=2; i<sqM+1; ++i) {
    if(p[i]) for(int j=i*i; j<M; j+=i) p[j] = false;
  }
  while(cin >> n && n) {
    int ans = 0;
    for(int i=2; i<n/2+1; ++i) {
      if(p[i]&&p[n-i]) ++ans;
    }
    cout << ans << endl;
  }
  return 0;
}