def pretty_print(poly):
    R_terms = []
    r_terms = []
    x_terms = []
    mixed_terms = []

    if isinstance(poly, int):
        return str(poly)

    has_const = bool(poly.constant_coefficient())

    for monom in poly:
        vars_in_term = [str(v) for v in monom.variables()]

        if not vars_in_term:
            continue

        term = "*".join(vars_in_term)
        families = {v[0] for v in vars_in_term}

        if families == {"R"}:
            R_terms.append(term)
        elif families == {"r"}:
            r_terms.append(term)
        elif families == {"x"}:
            x_terms.append(term)
        else:
            mixed_terms.append(term)

    parts = []

    if has_const:
        parts.append("1")

    if R_terms:
        parts.append("f(Ri)")

    if r_terms:
        parts.append("f(ri)")

    parts.extend(x_terms)
    parts.extend(mixed_terms)

    return " + ".join(parts) if parts else "0"


def pretty_print_vec(vec):
    return "[" + ",\n ".join(pretty_print(p) for p in vec) + "]"