code: 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