<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 ise(string g){
    map<char,int>mp;
    for(int i=0;i<g.size();i++)mp[g[i]]++;
    return mp.size()==g.size();
}
bool is(string m,string n){
    m+=n;
    map<char,int>mp;
    for(int i=0;i<m.size();i++)mp[m[i]]++;
    return mp.size()==m.size();
}
void solve(int ind,vector<string>& arr,int& maxi,string& h,unordered_map<string,int>&mpe){
    if(ind==arr.size())return ;
     string memoKey = h + to_string(ind);
    if(mpe.find(memoKey)!=mpe.end())return;
    for(int i=ind;i<arr.size();i++){

    if(i==0 && ise(arr[i]) || is(h,arr[i])==true && ise(arr[i])){
        h+=arr[i];
        maxi=max(maxi,static_cast<int>(h.size()));
        solve(i+1,arr,maxi,h,mpe);

                h.erase(h.size() - arr[i].size(), arr[i].size());  // Properly remove the added string
    }
    }
    solve(ind+1,arr,maxi,h,mpe);
    mpe[memoKey]=maxi;
}
    int maxLength(vector<string>& arr) {
        map<char,int>mp;
        int maxi=0;
        string h="";
        unordered_map<string,int> mpe;
        solve(0,arr,maxi,h,mpe);
        
        return maxi;
    }
};
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