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>
int table[500001];
int main(){
	table[1]=-1;
	table[0]=-1;
	for(int i=2;i<500001;i++){
		if(table[i]==0){
			table[i]=1;
			for(int j=i*2;j<500001;j+=i)table[j]=-1;
		}
	}
	int a;
	while(scanf("%d",&a),a){
		int ret=0;
		for(int i=1;i<=a/2;i++){
			if(table[i]==1&&table[a-i]==1)ret++;
		}
		printf("%d\n",ret);
	}
}