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
import math

num = 50000
L = [True] * (num+1)
L[0] = L[1] = False
sqrt = int(num**0.5) +1
for i in range(2, sqrt):
    if L[i] == False:
        continue
    for j in range(i*2,num+1,i):
        L[j] = False

p = [x for x in range(num+1) if L[x] ]

#pset = set(p)

while True:
    num = int(input())
    if num == 0:
        break

    half = num // 2
    c = 0
    for i in p:
        if i > half:
            break
        j = num - i
        if L[j]:
            c += 1
    print(c)

