def numberOfDigits(n):
    tot = 0
    while n:
        n/=10
        tot+=1
    return tot
def isValid(n):
    n_digits = numberOfDigits(n)
    if(n_digits < 13):
        return False
    if(n_digits > 16):
        return False
    # It is not one of the 4 credit card brands
    div = 10 ** (n_digits-1)
    div2 = 10 ** (n_digits-2)
    if (n / div != 4) and (n / div != 5) and (n / div != 6) and (n / div2 != 37):
        return False
    aux = n / 10
    tot = 0
    # steps 1 and 2
    while(aux):
        digit = aux % 10
        digit = digit * 2
        digit = digit/10 + digit % 10
        tot += digit
        aux /= 100

    # step 3 nad 4
    aux = n
    while(aux):
        tot += aux % 10
        aux /= 100

    if(tot % 10 == 0):
        return True
    return False

print isValid(100)
print isValid(4388576018410707)
print isValid(4388576018402626)