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

N = 50001
lst = [True] * N
lst[0] = False
lst[1] = False
for i in range(2, int(N ** 0.5) + 1):
    if lst[i]:
        for j in range(i * i, N, i):
            lst[j] = False

primes = [i for i in range(1, N) if lst[i]]

for s in sys.stdin:
    n = int(s)
    if n == 0:
        break
    elif n % 2 == 1:
        if lst[n - 2]:
            print(1)
        else:
            print(0)
    elif n == 4:
        print(1)
    else:
        counter = 0
        for prime0 in primes:
            prime1 = n - prime0
            if prime0 <= prime1 and lst[prime1]:
                #print(prime0, prime1)
                counter += 1
        print(counter)