<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:
    unordered_map<string, int> mp;
    bool common(string& str1, string& str2) {
        vector<int> vec(26, 0);

        for (auto& ch : str1) {
            if (vec[ch - 'a'] > 0)
                return true;
            vec[ch - 'a']++;
        }

        for (auto& ch : str2) {
            if (vec[ch - 'a'] > 0)
                return true;
            vec[ch - 'a']++;
        }
        return false;
    }

    int solve(int idx, vector<string>& arr, string& temp) {
        int n = arr.size();
        if (idx >= n)
            return temp.size();
        int inc = 0;
        int exc = 0;

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

        if (common(arr[idx], temp))
            exc = solve(idx + 1, arr, temp);
        else {
            exc = solve(idx + 1, arr, temp);
            string org = temp;
            temp += arr[idx];
            inc = solve(idx + 1, arr, temp);
            temp = org;
        }
        return mp[temp] = max(inc, exc);
    }

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