<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>


int maxLen(vector<string>& arr, unordered_set<char> exclusionChars) {
    // return max len, where the given unordered_set of chars cannot be used

    // base case
    if (arr.size() == 0) {
        return 0;
    }

    // consider what to do with arr[0], then recurse on remainder of problem

    // first, what happens if we don't take arr[0]
    auto arrTail = vector<string>(arr.begin()+1, arr.end());
    int leaveIt = maxLen(arrTail, exclusionChars);

    // next, what happens if we *do* take arr[0]
    int takeIt;
    int nExclusions = exclusionChars.size();
    for (auto c : arr[0]){
        exclusionChars.insert(c);
    }
    if (exclusionChars.size() != nExclusions + arr[0].size()){
        // cannot take it - arr[0] chars present in exclusions
        takeIt = -1;
    } else {
        takeIt = maxLen(arrTail, exclusionChars) + arr[0].size();
    }
    
    return max(takeIt, leaveIt);

}

class Solution {
public:
    int maxLength(vector<string>& arr) {
        unordered_set<char> exclusions;
        return maxLen(arr, exclusions);
    }
};
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