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
def make_tbl(n):
    tbl = [False, True, False, False, False, True] * (n // 6 + 1)
    for i in range(1, 4):
        tbl[i] = not tbl[i]
    p, stp, sqrt = 5, 2, n ** 0.5
    while p < sqrt:
        for i in range(p ** 2, n, 2 * p):
            tbl[i] = False
        while True:
            p += stp
            stp = 6 - stp
            if tbl[p]:
                break
    return tbl
tbl = make_tbl(50000)
ps = [i for i in range(50000) if tbl[i]]
while True:
    n = int(input())
    if not n:
        break
    res = 0
    if n % 2:
        if tbl[n - 2]:
            res += 1
    else:
        res = 0
        for p in ps:
            if 2 * p > n:
                break
            if tbl[n - p]:
                res += 1
    print(res)