Set $ q_i = p_i - (i-1) $, then $ q_1 < q_2 < q_3 $ in $ \1,\dots,3\ $, since $ p_3 \le 8 $, $ q_3 \le 8 - 2 = 6 $, but $ q_1 \ge 1 $, $ q_3 \ge q_2 + 2 \ge 1+2=3 $, $ q_3 \le 3 + 2 = 5 $? Let's see: - Crosslake