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>
#include<algorithm>
#include<vector>
#include<map>
#include<cstring>
using namespace std;

#define rep(i,n) for(int i=0;i<n;i++)
#define REP(n) rep(i,n)
#define all(n) n.begin(),n.end()

const int MAXN = 50100;

bool p[MAXN];

int main()
{
    p[0] = p[1] = 1;
    REP(MAXN)if(!p[i])for(int j = i*2;j<MAXN;j+= i) p[j] = 1;

    int n;
    while(cin >> n && n)
    {
        int ans = 0;
        for(int i = 2;i <= n/2 ;i++) ans += (!p[i]) &(!p[n - i]);

        cout << ans << endl;
    }

    return 0;
}