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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def solve_mbar_for_all_states(u_kn, N_k, f_k, solver_protocol):
 """Solve for free energies of states with samples, then calculate for empty states. Parameters u_kn : np.ndarray, shape=(n_states, n_samples), dtype='float' The reduced potential energies, i.e. -log unnormalized probabilities N_k : np.ndarray, shape=(n_states), dtype='int' The number of samples in each state f_k : np.ndarray, shape=(n_states), dtype='float' The reduced free energies of each state solver_protocol: tuple(dict()), optional, default=None Sequence of dictionaries of steps in solver protocol for final stage of refinement. Returns ------- f_k : np.ndarray, shape=(n_states), dtype='float' The free energies of states """

    states_with_samples = np.where(N_k > 0)[0]

    if len(states_with_samples) == 1:
        f_k_nonzero = np.array([0.0])
    else:
        f_k_nonzero, all_results = solve_mbar(u_kn[states_with_samples], N_k[states_with_samples],
                                              f_k[states_with_samples], solver_protocol=solver_protocol)

    f_k[states_with_samples] = f_k_nonzero

    # Update all free energies because those from states with zero samples are not correctly computed by solvers.
    f_k = self_consistent_update(u_kn, N_k, f_k)
    # This is necessary because state 0 might have had zero samples,
    # but we still want that state to be the reference with free energy 0.
    f_k -= f_k[0]

    return f_k