<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 {
    unordered_map<string, int> mpp;

    bool isPos(string s1, string s2)
    {
        vector<int> hash(26, 0);
        for(int i=0; i<s1.size(); i++)
        {
            if(hash[s1[i]-'a'] != 0) return false;
            hash[s1[i]-'a']++;
        }

        for(int i=0; i<s2.size(); i++)
        {
            if(hash[s2[i]-'a'] != 0) return false;
            hash[s2[i]-'a']++;
        }
        return true;
    }

    int f(int ind, string str, vector<string> arr, int n)
    {
        if(ind==n) return str.length();
        
        if(mpp.find(str)!= mpp.end()) return mpp[str];
        
        int notake = 0+ f(ind+1, str, arr, n);
        int take = -1e9;
        if( isPos(str, arr[ind]))
        {
            take = f(ind+1, str + arr[ind], arr, n);
        }
        
            
        return mpp[str] = max(take, notake);

    }
public:
    int maxLength(vector<string>& arr) {
        int n = arr.size();
        string str = "";
        mpp.clear();
        return f(0, str, arr, n);
    }
};
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