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You are given an array words of strings.

A move onto s consists of swapping any two even indexed characters of s, or any two odd indexed characters of s.

Two strings s and t are special-equivalent if after any number of moves onto s, s == t.

For example, s = "zzxy" and t = "xyzz" are special-equivalent because we may make the moves "zzxy" -> "xzzy" -> "xyzz" that swap s[0] and s[2], then s[1] and s[3].

Now, a group of special-equivalent strings from words is a non-empty subset of words such that:

  1. Every pair of strings in the group are special equivalent, and;
  2. The group is the largest size possible (ie., there isn't a string s not in the group such that s is special equivalent to every string in the group)

Return the number of groups of special-equivalent strings from words.

 

Example 1:

Input: words = ["abcd","cdab","cbad","xyzz","zzxy","zzyx"]
Output: 3
Explanation: 
One group is ["abcd", "cdab", "cbad"], since they are all pairwise special equivalent, and none of the other strings are all pairwise special equivalent to these.

The other two groups are ["xyzz", "zzxy"] and ["zzyx"].  Note that in particular, "zzxy" is not special equivalent to "zzyx".

Example 2:

Input: words = ["abc","acb","bac","bca","cab","cba"]
Output: 3

 

Note:

  • 1 <= words.length <= 1000
  • 1 <= words[i].length <= 20
  • All words[i] have the same length.
  • All words[i] consist of only lowercase letters.

class Solution { public int numSpecialEquivGroups(String[] words) { } }