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
import sys

N = 50000
t = [1]*(N)
p = [2]
d = {2:1}
for i in range(3, N, 2):
    if t[i]:
        p.append(i)
        d[i] = 1
        for j in range(3*i, N, 2*i): t[j] = 0

while True:
    n = int(sys.stdin.readline())
    if n == 0: break

    count = 0
    if n % 2:
        if n - 2 in p: count += 1
    else:
        for p1 in p:
            if 2*p1 > n: break
            if n - p1 in d:
                count += 1
    print(count)