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<bitset>
int main()
{
	const int N=50001;
	int i,j,n,c;
	std::bitset<N>p(3);
	p.flip();
	for(i=2;i*i<N;++i)if(p[i])for(j=i*2;j<N;j+=i)p[j]=0;
	while(scanf("%d",&n),n)
	{
		for(c=i=0,j=n;i<=j;++i,--j)if(p[i]&&p[j])++c;
		printf("%d\n",c);
	}
	return 0;
}