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;

bool prime[100010];
int ans[100010];
void countPrime();

int main(){
  int n;
  countPrime();
  while(cin >> n , n){
    cout << ans[n] << endl;
  }
}

void countPrime(){
  memset(prime,true,100001);
  memset(ans,0,100001);
  for(int i=2;i*i<=50000;i++){
    if(prime[i]){
      for(int j=i*i;j<=50000;j=j+i){
	prime[j]=false;
      }
    }
  }
  for(int i=2;i<50000/2+1;i++){
    for(int j=i;j<50000+1;j++){
      if(prime[i] && prime[j]){
	ans[i+j]++;
      }
    }
  }
}