<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 insertinto(string s,vector<int>&arr)
    {
        int n=s.size();
        vector<int>trr(26);
        trr=arr;
        
        for(int i=0;i<n;i++)
        {
            if(trr[s[i]-'a']>0) return false;
           else {
                    trr[s[i]-'a']+=1;
            }
        }
        return true;
    }
    vector<int>doit(string s,vector<int>&arr)
    {
         int n=s.size();
        for(int i=0;i<n;i++)
        {
            arr[s[i]-'a']+=1;
        }
        return arr;
    }
     vector<int> undo(string s,vector<int>&arr)
    {
        int n=s.size();
        for(int i=0;i<n;i++)
        {
             arr[s[i]-'a']-=1;
        }
        return arr;
    }
    int solve(vector<string>&str,int n,vector<int>&arr,int idx)
    {
        if(idx==n)return 0;
        int take=0;
        if(insertinto(str[idx],arr))
        {
         arr=doit(str[idx],arr);
        take=str[idx].size()+solve(str,n,arr,idx+1);
        arr=undo(str[idx],arr);
        }
        int notake=solve(str,n,arr,idx+1);
        return max(take,notake);
    }
    int maxLength(vector<string>& str) {
        vector<int>arr(26,0);
        int n=str.size();
        return solve(str,n,arr,0);
    }
};
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