def nthVampireNumber(n):
    guess = 0
    found = 0
    while found <= n:
        guess += 1
        if isVampireNumber(guess):
            found += 1
    return guess

def isVampireNumber(n):
    for factor1 in range(1, sqrt(n)+1):
        if n%factor1 == 0:
            factor2 = n//factor1
            if not (factor1 % 10 == 0 and factor2 % 10 == 0):
                if goodLengths(factor1, factor2, n):
                    if canRearrange(factor1, factor2, n):
                        return True
    return False

def goodLengths(f1, f2, n):
    return digitCount(f1) == digitCount(f2) == (1/2)*digitCount(n)

def digitCount(n):
    count = 0
    while n > 0:
        count += 1
        n//10
    return count

def canRearrange(f1, f2, n):
    overallString = str(f1) + str(f2)
    n = str(n)

    for digit in overallString:
        if overallString.count(digit) != n.count(digit):
            return False
    return True