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>
#define N 50000
using namespace std;

bool isP[N+1];

void make_isP(){
  isP[0]=isP[1]=false;
  for(int i=2;i<=N;i++)isP[i]=true;
  for(int i=2;i*i<=N;i++){
    if(!isP[i])continue;
    for(int j=i*i;j<=N;j+=i)isP[j]=false;
  }
}

int main(){
  make_isP();
  //for(int i=0;i<=20;i++)cout<<i<<" "<<isP[i]<<endl;
  int n,cnt;
  while(cin>>n&&n){
    
    cnt=0;
    for(int i=0;i<=n/2;i++){
      if(isP[i]&&isP[n-i]){
	cnt++;
      }
    }
    cout<<cnt<<endl;
  }
  return 0;
}