<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 unique(string A, string B) {
        unordered_set<char> stA;
        for (char c : A) {
            if (stA.find(c) != stA.end()) return false;
            stA.insert(c);
        }

        unordered_set<char> stB;
        for (char c : B) {
            if (stB.find(c) != stB.end()) return false;
            stB.insert(c);
        }

        for (char c : B) {
            if (stA.find(c) != stA.end()) return false;
        }

        return true;
    }

    unordered_map<string,int> t;

    int topDown(vector<string>& arr, string temp, int curr, int n) {
        if (curr >= n) return temp.length();

        if(t.find(temp)!=t.end()) return t[temp];

        int take = 0;
        if (unique(temp, arr[curr])) {
            take = topDown(arr, temp + arr[curr], curr + 1, n);
        }

        int notake = topDown(arr, temp, curr + 1, n);

        return t[temp] = max(take, notake);
    }
    
    int maxLength(vector<string>& arr) {
        t.clear();
        int n = arr.size();
        return topDown(arr,"",0,n);
    }
};
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