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<cstdio>
#include<bitset>
using namespace std;

bitset<50001> pt;

void MakeTable(int n){
  pt.reset();
  pt.set(2);
  
  int i;
  for(i=3;i<=n;i+=2)pt.set(i);
  
  i = 3;
  while(i*i<=n){
    for(int j=3*i;j<=n;j+=i)pt.reset(j);
    while(!pt[++i]);
  }
}

int main(){
  int n,ans;
  MakeTable(50000);

  while(scanf("%d",&n) && n){
    if(n&1)pt[n-2]?printf("1\n"):printf("0\n");
    else{
      ans = 0;
      for(int i=0;i<=n/2;i++)
	if(pt[i] && pt[n-i])ans++;
      printf("%d\n",ans);
    }
  }
}
	