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>
#include <vector>

using namespace std;

bool isPrime[1000000];

int main(void){
  vector<int> pvec;
  //但多
  fill(isPrime,isPrime+1000000,true);
  for(int i=2;i<=50000;i++){
    if(isPrime[i] == true){
      pvec.push_back(i);
      for(int j=2;i*j<1000000;j++){
	isPrime[i*j] = false;
      }
    }
  }
  int tmp;
  while(cin >> tmp){
    int ret = 0;
    if(!tmp) break;
    for(int i=0;pvec[i]*2 <= tmp;i++){
      if(binary_search(pvec.begin(), pvec.end(), tmp-pvec[i])) ret++;
    }
    cout << ret << endl;
  }
}