<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 {
public:
    bool duplicate(string& str, string &temp) {
        int arr[26] = {0};
        for (auto &i : temp) {
            if (arr[i - 'a'] > 0) return true;
            arr[i - 'a']++;
        }
        for (auto &i : str) {
            if (arr[i - 'a'] > 0) return true;
            arr[i - 'a']++;
        }
        return false;
    }
        unordered_map<string, int> mp;

    int dfs(vector<string>& vec, int i, string &str) {
        int n = vec.size();
        if (i >= n) return str.size();
        if(mp.find(str) != mp.end())
            return mp[str];
        int include = 0;
        int exclude = 0;
        if (duplicate(str, vec[i])) {
            exclude = dfs(vec, i + 1, str);
        } else {
            exclude = dfs(vec, i + 1, str);
            str += vec[i];
            include = dfs(vec, i + 1, str);
            str.erase(str.size() - vec[i].size()); // Backtrack
        }
        return mp[str]=max(include, exclude);
    }

    int maxLength(vector<string>& arr) {
        string temp = "";
        mp.clear();
        return dfs(arr, 0, temp);
    }
};

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