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
from math import sqrt, floor

p = [2]
for i in range(3, 50000, 2):
    for j in range(3, floor(sqrt(i)) + 1, 2):
        if not i % j:
            break
    else:
        p.append(i)
sp = set(p)

while True:
    n = int(input())
    if not n:
        break
    if n & 1:
        print(int(n - 2 in sp))
        continue
    n2 = n // 2
    cnt = 0
    for i in p:
        if n2 < i:
            break
        if n - i in sp:
            cnt += 1
    print(cnt)