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 bisect,sys
from itertools import *
n=range(50001);a=list(n);a[1]=0
for i in range(2,224):a[i*2::i]=[0]*len(a[i*2::i])
p=list(compress(n,a))
for x in map(int,sys.stdin):
 if x:print(sum(1 for d in p[:bisect.bisect(p,x//2)]if a[x-d]))
