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
def primes(n):
  l = [1 for i in range(n+1)]
  l[0] = l[1] = 0
  for i in range(2,int((n)**(1/2))+1):
    if l[i] == 1:
      for j in range(2,n//i+1):
        l[i*j] = 0
  return l

l = primes(50000)
while True:
  n = int(input())
  if n == 0:
    break
  count = 0
  if not(n%2):
    for i in range(3,n//2+1,2):
      if (l[i] and l[n-i]):
        count += 1
    if n == 4:
      count = 1
  else:
    if l[n-2]:
      count += 1
  print(count)