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 <algorithm>
using namespace std;

const int MAXN = 50005;
bool isP[MAXN];

int main() {
  fill(isP, isP+MAXN, true);
  isP[0] = isP[1] = false;
  for(int i = 0; i < MAXN; ++i) {
    if(!isP[i]) continue;
    for(int j = i*2; j < MAXN; j += i) isP[j] = false;
  }
  int n;
  while(cin >> n && n) {
    int res = 0;
    for(int i = 2; i <= n-i; ++i) {
      if(isP[i] && isP[n-i]) {
        ++res;
      }
    }
    cout << res << endl;
  }
  return 0;
}