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 <vector>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

#define NUM (60000)
int pt[NUM];
int cnt[NUM];

int main() {
    vector<int> ps;
    for (int i = 2; i < NUM; i++) if (pt[i] == 0) {
        ps.push_back(i);
        for (int j = i+i; j < NUM; j+=i) pt[j] = i;
    }
    rep (i, ps.size()) rep (j, i+1) {
        if (ps[i]+ps[j] >= NUM) break;
        cnt[ps[i]+ps[j]]++;
    }
    for (;;) {
        int n;
        scanf("%d", &n);
        if (n == 0) return 0;
        printf("%d\n", cnt[n]);
    }
}