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 itertools import *

def sieve(n):
    a = range(n)
    a[:2] = None, None
    for i in range(2, n):
        if i ** 2 >= n: break
        if not a[i]: continue
        for i in range(i ** 2, n, i):
            a[i] = None
    return a

b = sieve(50000)
a = [v for v in b if v]
while True:
    n = int(raw_input())
    if n == 0: break
    ct = 0
    for v in a:
        if v > n / 2: break
        if b[n - v]:
            ct += 1
    print ct