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 = [True for i in range(50000)]
p[0] = 0
for i in range(2,int(50000**(1/2)+1)):
    if p[i-1]:
        for j in range(i**2,50000,i):
            p[j-1] = False

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

while(1):
    n = int(input())
    if not n:
        break
    count = 0
    half = n//2
    for i in prime:
        if i > half:
            break
        if p[n - i - 1]:
            count += 1
    print(count)
