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>
#define REP(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) REP(i, 0, n)
bool p[50001];
int main()
{
	rep(i, 50001) p[i] = true;
	for (int i = 2; i * i <= 50000; ++i) {
		if (p[i]) for (int j = 2 * i; j <= 50000; j += i)
			if (p[j]) p[j] = false;
	}
	p[0] = p[1] = false;

	int n;
	while (scanf("%d", &n), n) {
		int c = 0;
		REP(i, 2, n/2+1) if (p[i] && p[n-i]) c++;
		printf("%d\n", c);
	}
	return 0;
}