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<stdio.h>
#include<string.h>

char so[50001];

int main(){
	memset(so,0,sizeof(so));
	
	int n,i,j,count;
	for(i=2;i<225;i++){
		for(j=i;j*i<=50000;j++){
			so[j*i]=1;
		}
	}
	
	while(~scanf("%d",&n)){
		if(n==0)break;
		count=0;
		for(i=2;i<(n>=25000 ? 25000:n);i++){
			if(i>n-i)break;
			if(so[i]==0 && so[n-i]==0){
				++count;
			}
		}
		printf("%d\n",count);
	}
	return 0;
}