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
n = 50001
is_prime = [i for i in range(n)]
is_prime[0] = is_prime[1] = 0
i = 2
while i**2 <= n:
    j = i*2
    while j < n:
        is_prime[j] = 0
        j += i
    i += 1

prime_set  = set(is_prime)
prime_set.remove(0)
prime_list = sorted(list(prime_set))

while True:
    cnt = 0
    n = int(input())
    if n == 0:
        break
    for i in prime_list:
        if i > n//2:
            break
        if n - i in prime_set:
            cnt += 1
    print(cnt)

