Well, I've been trying to solve this problem from USACO January Bronze Division. I think this is a LIS-related problem, so I tried using Dilworth's theorem. The thing is, even if I can calculate the length of the longest anti-chain according to the Cowphabet sequence (using binary search like any other LIS problem), I keep getting these annoying Wrong Answers ... Can you tell me where did a make a mistake ? I can't even figure out under what circumstance my approach would fail, but apparently it seem to be a false solution.

P/S : Yep, this problem can be solved using an O(N^2) approach, but I'm trying to do it with a O(NlogN) ... Anyway, help pls.

EDIT: Uh, and just to clarify, by LIS i mean Longest Increasing Subsequence.