def nativeCliqueEmbed(self, width):
        maxCWR = {}
        M, N = self.M, self.N
        maxscore = None
        count = 0
        key = None
        for w in range(width + 2):
            h = width - w - 2
            for ymin in range(N - h):
                ymax = ymin + h
                for xmin in range(M - w):
                    xmax = xmin + w
                    R = (xmin, xmax, ymin, ymax)
                    score, best = self.maxCliqueWithRectangle(R, maxCWR)
                    maxCWR[R] = best
                    if maxscore is None or (score is not None and maxscore < score):
                        maxscore = score
                        key = None
                        count = 0
                    if maxscore == score:
                        count, key = _accumulate_random(count, best[3], key, R)
        clique = []
        while key in maxCWR:
            score, ell, key, num = maxCWR[key]
            if ell is not None:
                meb = self.maximum_ell_bundle(ell)
                clique.extend(meb)
        return maxscore, clique