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
primes = [0, 0] + [1] * 49999
for i in range(2, 224):
    if primes[i]:
        for j in range(i*i, 50001, i):
            primes[j] = 0
values = [i for i, k in enumerate(primes) if k]
while True:
    n = int(input())
    if n == 0:
        break
    I = bisect.bisect(values, n//2)
    print(len([1 for v in values[:I] if primes[n-v]]))