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 $W$.

-----Input-----
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-----
Output the size of the largest swap-free set.

-----Examples-----
Sample Input 1:
6
abc
acb
cab
cba
bac
bca
Sample Output 1:
3

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

Source: kattis | Difficulty: MEDIUM


Solutions: