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
p = [1] * (50000 + 1)
p[0], p[1] = 0, 0
for i in range(2, int(50000 ** 0.5) + 1):
    if not p[i]:
        continue
    for j in range(2 * i, 50000 + 1, i):
        p[j] = 0

p_num = [i for i in range(50000 + 1) if p[i] == 1]


while 1:
    n = int(input())
    if (n == 0):
        break
    cnt = 0
    for i in p_num:
        if n // 2 < i:
            break
        if p[n - i]:
            cnt += 1
    print(cnt)

