<p>You are given an array of strings <code>arr</code>. A string <code>s</code> is formed by the <strong>concatenation</strong> of a <strong>subsequence</strong> of <code>arr</code> that has <strong>unique characters</strong>.</p>

<p>Return <em>the <strong>maximum</strong> possible length</em> of <code>s</code>.</p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [&quot;un&quot;,&quot;iq&quot;,&quot;ue&quot;]
<strong>Output:</strong> 4
<strong>Explanation:</strong> All the valid concatenations are:
- &quot;&quot;
- &quot;un&quot;
- &quot;iq&quot;
- &quot;ue&quot;
- &quot;uniq&quot; (&quot;un&quot; + &quot;iq&quot;)
- &quot;ique&quot; (&quot;iq&quot; + &quot;ue&quot;)
Maximum length is 4.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [&quot;cha&quot;,&quot;r&quot;,&quot;act&quot;,&quot;ers&quot;]
<strong>Output:</strong> 6
<strong>Explanation:</strong> Possible longest valid concatenations are &quot;chaers&quot; (&quot;cha&quot; + &quot;ers&quot;) and &quot;acters&quot; (&quot;act&quot; + &quot;ers&quot;).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [&quot;abcdefghijklmnopqrstuvwxyz&quot;]
<strong>Output:</strong> 26
<strong>Explanation:</strong> The only string in arr has all 26 characters.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 16</code></li>
	<li><code>1 &lt;= arr[i].length &lt;= 26</code></li>
	<li><code>arr[i]</code> contains only lowercase English letters.</li>
</ul>

class Solution:
    def maxLength(self, arr: List[str]) -> int:
        
        def encode(word):
            letter_count = defaultdict(lambda: 0)
            for letter in word:
                letter_count[letter] += 1
                if letter_count[letter] > 1:
                    return None
            bitmap = 0
            for letter in letter_count:
                bitmap += 2 ** (ord(letter) - ord('a'))
            return bitmap
        
        answers = defaultdict(lambda: 0)
        for word in arr:
            
            bitmap = encode(word)
            if not bitmap:
                continue
            
            # New word alone
            new_answers = answers.copy()
            if len(word) > new_answers[bitmap]:
                new_answers[bitmap] = len(word)

            # New word concatenated to other words
            for bitmap0 in answers:
                if bitmap & bitmap0:
                    continue
                new_bitmap = bitmap | bitmap0
                new_length = answers[bitmap0] + len(word)
                if new_length > new_answers[new_bitmap]:
                    new_answers[new_bitmap] = new_length
            
            answers = new_answers
        
        res = 0
        for value in answers.values():
            res = max(res, value)
        return res
22700