function [xmin, xmax] = maxlist_eval(x, L)

mode = 1;
for s=1:2
    mode = -mode;
    
    P = mode*1234;
    u = zeros(L, 1);
    p = zeros(L, 1);
    u_last = zeros(L, 1);
    p_last = zeros(L, 1);

    OFF = 1;

    u_last(1 + OFF) = P;
    u_last(0 + OFF) = 0;
    p_last(0 + OFF) = 0 + OFF;
    N = 0 + OFF;

    for k=1:lge(x),
        if (p_last(N) == (L + OFF))
            m = 0;
            u_last(N) = P;
        else
            m = 1;
        end

        ii = 0;
        while mode*x(k) >= mode*u_last(ii+1+OFF)
            ii = ii + 1;
        end
        N = N - ii + m;

        for jj=(1 + OFF):(N -1)
            u(jj+1) = u_last(jj+ii);
            p(jj+1) = p_last(jj+ii) + 1;
        end
        u(N+1) = P;
        u(1 + OFF) = x(k);
        p(1 + OFF) = 1 + OFF;
        u_last = u;
        p_last = p;
        if (mode < 0)
            xmin(k) = u(N);
            pmmin = p(N);
        else
            xmax(k) = u(N);
            pmax = p(N);
        end
    end;
end;