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
from bisect import bisect_right
from itertools import chain, compress

ub = 50000
is_prime = [0, 0, 1, 1] + [0]*(ub-3)
is_prime[5::6] = is_prime[7::6] = [1]*int(ub/6)
primes = [2, 3]
append = primes.append

for n in chain(range(5, ub, 6), range(7, ub, 6)):
    if is_prime[n]:
        append(n)
        is_prime[n*3::n*2] = [0]*((ub-n)//(n*2))
primes.sort()

for n in map(int, sys.stdin):
    if not n:
        break
    if n%2:
        print(is_prime[n-2])
    else:
        print(len([1 for p in primes[:bisect_right(primes, n/2)] if is_prime[n-p]]))
