sub is_compatible {
    my T, B;
    foreach i from 0 .. stringlen {
        next if top[i] eq bottom[i]
        if top[i] is a digit
            return NOT COMPATIBLE if bottom[i] is a digit
            T |= top[i]
        if bottom[i] is a digit
            B |=  bottom[i]
    }
    return T&B ? NOT COMPATIBLE : COMPATIBLE
}