<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:
    map<pair<int,string>,int> mp;
    bool hasdup(string &s1,string &s2)
    {
        vector<int> ch(26,0);
        for(auto &it: s1)
        {
            if(ch[it-'a']>0)
            {
                return true;
            }

            ch[it-'a']++;
        }

        for(auto &it: s2)
        {
            if(ch[it-'a']>0)
            return true;
        }

        return false;
    }
    int f(int i,string temp,vector<string> &arr)
    {
        if(i==arr.size())
        return temp.size();

        if(mp.find({i,temp})!=mp.end())
        return mp[{i,temp}];

        int include=0;
        int exclude=0;

        if(hasdup(arr[i],temp))
        {
            exclude=f(i+1,temp,arr);
        }
        else
        {
            exclude=f(i+1,temp,arr);
            include=f(i+1,temp+arr[i],arr);
        }

        return mp[{i,temp}]=max(include,exclude);
    }
    int maxLength(vector<string>& arr) {

        string temp="";
        return f(0,temp,arr);
        
    }
};
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