<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 poss(const string &s, const string &a) {
        unordered_set<char> p(s.begin(), s.end());
        for (char c : a) {
            if (p.find(c) != p.end()) {
                return false;
            }
        }
        return true;
    }
    bool check(string &s)
    {
          unordered_set<char> p(s.begin(), s.end());
          if(p.size()<s.size())
          return false;
          return true;
    }

    int rec(vector<string>& arr, int i, string s, unordered_map<string, int>& memo) {
        string state = to_string(i) + ":" + s;
        if (memo.find(state) != memo.end()) {
            return memo[state];
        }
        if (i >= arr.size()) {
            return 0;
        }

        int nottake = rec(arr, i + 1, s, memo);
        int take = 0;
        if (poss(s, arr[i])&& check(arr[i])) {
            take = arr[i].size() + rec(arr, i + 1, s + arr[i], memo);
        }

        memo[state] = max(take, nottake);
        return memo[state];
    }

    int maxLength(vector<string>& arr) {
        unordered_map<string, int> memo;
        string s = "";
        return rec(arr, 0, s, memo);
    }
};

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