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
def sieve(m):
    N=range(1,m+2,2)
    r=int(m**.5)
    h=len(N)
    N[0]=0
    i=0
    while i<h:
        x=N[i]
        if x>r: break
        if x and i+x<h: N[i+x:h:x]=[0]*((h-1-i-x)/x+1)
        i+=1
    return N
def f0056(n):
    x=0
    if n<4:x=0
    elif n==4:x=1
    elif n%2:
        if S[(n-2)/2]: x=1
    else:
        a=n/2
        for e in PRIMES:
            if e>a: break
            if S[(n-e)/2]: x+=1
    return x

S=sieve(50000)
PRIMES=filter(None,S)
for n in sys.stdin:
    n=int(n)
    if n==0: break
    print f0056(n)