def multiply(phi1, phi2):
    assert isinstance(phi1, Factor) and isinstance(phi2, Factor)
    # Cerinta 1 :
    new_vars = []
    new_values = {}

    for var in phi1.vars:
        new_vars.append(var)
    for var in phi2.vars:
        if var not in phi1.vars:
            new_vars.append(var)

    for values1 in phi1.values:
        for values2 in phi2.values:
            ok = True
            for var in new_vars:
                if var in phi1.vars and var in phi2.vars:
                    idx1 = phi1.vars.index(var)
                    idx2 = phi2.vars.index(var)
                    if values1[idx1] != values2[idx2]:
                        ok = False

            if ok:
                tmp_val = []
                for var in new_vars:
                    if var in phi1.vars:
                        idx1 = phi1.vars.index(var)
                        tmp_val.append(values1[idx1])
                    else:
                        idx2 = phi2.vars.index(var)
                        tmp_val.append(values2[idx2])
                new_values[tuple(tmp_val)] = phi1.values[values1] * phi2.values[values2]

    result = Factor(new_vars, new_values)
    return result