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You are given $W$, a set of $N$ words that are anagrams of each other. There are no duplicate letters in any word. A set of words $S \subseteq W$ is called "swap-free" if there is no way to turn a word $x \in S$ into another word $y \in S$ by swapping only a single pair of (not necessarily adjacent) letters in $x$. Find the size of the largest swap-free set $S$ chosen from the given set $W$.
The first line of input contains an integer $N$ ($1 \le N \le 500$). Following that are $N$ lines each with a single word. Every word contains only lowercase English letters and no duplicate letters. All $N$ words are unique, have at least one letter, and every word is an anagram of every other word.
Output the size of the largest swap-free set.
6 abc acb cab cba bac bca
11 alerts alters artels estral laster ratels salter slater staler stelar talers
6 ates east eats etas sate teas