"""
You are given an array of strings arr. A string s is formed by the concatenation of a subsequence of arr that has unique characters.
Return the maximum possible length of s.
A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Example 1:
Input: arr = ["un","iq","ue"]
Output: 4
Explanation: All the valid concatenations are:
- ""
- "un"
- "iq"
- "ue"
- "uniq" ("un" + "iq")
- "ique" ("iq" + "ue")
Maximum length is 4.

Example 2:
Input: arr = ["cha","r","act","ers"]
Output: 6
Explanation: Possible longest valid concatenations are "chaers" ("cha" + "ers") and "acters" ("act" + "ers").
Example 3:

Input: arr = ["abcdefghijklmnopqrstuvwxyz"]
Output: 26
Explanation: The only string in arr has all 26 characters.


Constraints:
1 <= arr.length <= 16
1 <= arr[i].length <= 26
arr[i] contains only lowercase English letters.

hints:
1 You can try all combinations and keep mask of characters you have.
2 You can use DP.
"""
from typing import List


class MaximumLengthOfaConcatenatedStringWithUniqueCharacters:
    def maxLength(self, arr: List[str]) -> int:
        dp = [set()]
        for word in arr:
            if len(set(word)) < len(word):
                continue
            word = set(word)
            for candidates in dp[:]:
                if word & candidates:
                    continue
                dp.append(candidates | word)
        return max(len(candidates) for candidates in dp)