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 <iostream>
#include <string.h>
#include <algorithm>
#define MAX 50000
using namespace std;

int dp[MAX + 1];
int prm[MAX + 1];

int main()
{
    for (int i = 2; i <= MAX; i++) prm[i] = 1;
    for	(int i = 2; i <= MAX; i++)
        for (int j = 2;	j * i <= MAX; j++)
            prm[i * j] = 0;
    int n;
    for (int i = 0; i <= MAX; i++)
        for (int j = i; j + i<= MAX; j++)
            if (prm[i] == 1 && prm[j] == 1) dp[i + j]++;
    while (cin >> n, n > 0) {
        cout << dp[n] << endl;
    }

    return 0;
}