<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:
        duplicate_set = set([])
        word_counter = {}
        for s in arr:
            counter = [0 for i in range(26)]
            for i in  range(len(s)):
                c = s[i]
                c_ind = ord(c)-ord('a')
                if counter[c_ind] >1:
                    duplicate_set.add(s)
                    break
                else:
                    counter[c_ind] += 1
            if s not in duplicate_set:
                word_counter[s] = counter    
        #print(word_counter)
        #print(duplicate_set)
        def helper(cur_arr_ind, char_counter, ex_len):
            nonlocal duplicate_set
            nonlocal word_counter
            if cur_arr_ind > len(arr)-1:
                return ex_len
            if ex_len > 25:
                return ex_len
            max_len = ex_len
            for i in range(cur_arr_ind, len(arr)):
                if arr[i] in duplicate_set:
                    continue
                
                cur_w = arr[i]
                cur_counter = word_counter[cur_w]
                go_next = True
                for k in range(26):
                    char_counter[k] += cur_counter[k]

                    if char_counter[k] >1:
                        for j in range(k+1):
                            char_counter[j] -= cur_counter[j]
                        go_next = False
                        break
                
                #print('curr_arr_ind',cur_arr_ind,'cur ind',i,'ex_len',ex_len,'charcounter:',char_counter)
                if go_next:
                    #print('went next curr_arr_ind',cur_arr_ind,'cur ind',i,'ex_len',ex_len,'charcounter:',char_counter)
                    temp = helper(i+1, char_counter, ex_len+len(cur_w))
                    max_len = max(max_len, temp)
                    for k in range(26):
                        char_counter[k] -= cur_counter[k]
                    #print('cleaned',char_counter)
            return max_len
        
        return helper(0, [0 for i in range(26)], 0)



        

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