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 sys
f = sys.stdin

def create_prime(n):
    prime = [1] * (n + 1)
    prime[:2] = [0, 0]
    for i in range(len(prime)):
        if prime[i]:
            for j in range(2 * i, len(prime), i):
                prime[j] = 0
    return prime

sieve = create_prime(50000)

prime = []
for i in range(25001):
    if sieve[i]:
        prime.append(i)

while True:
    n = int(f.readline())
    if n == 0:
        break
    cnt = 0
    temp = n // 2
    for i in prime:
        if i > temp:
            break
        if sieve[n - i]:
            cnt += 1
    print(cnt)