Code Names

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.

Sample Input 1 | Sample Output 1 |
---|---|

6 abc acb cab cba bac bca |
3 |

Sample Input 2 | Sample Output 2 |
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11 alerts alters artels estral laster ratels salter slater staler stelar talers |
8 |

Sample Input 3 | Sample Output 3 |
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6 ates east eats etas sate teas |
4 |