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 isPrime[50000];
int a[100000];
void func(){
	for(int i = 0; i < 50000; i++)isPrime[i] = 1;
	isPrime[0] = 0;
	isPrime[1] = 0;
	
	for(int i = 4; i < 50000; i++){
		for(int j = 2; j*j <= i; j++){
			if(i % j == 0){
				isPrime[i] = 0;
				break;
			}
		}
	}
	
	for(int i = 0; i < 50000; i++){
		for(int j = i; j < 50000; j++){
			if(isPrime[i]&&isPrime[j])a[i+j]++;
		}
	}
}


int x;
int main(void){
	
	int n;
	func();
	while(scanf("%d", &n),n){
		printf("%d\n", a[n]);
	}
}