<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 checkValidity(string s, string result){
        
        set<char> st;
        
        for(int i=0; i<result.length(); i++){
            
            if(st.find(result[i])!=st.end()){
                return false;
            }
            
            st.insert(result[i]);   
        }

        for(int i=0; i<s.length(); i++){
            if(st.find(s[i])!=st.end()){
                return false;
            }
        }

        return true;
    }

    int backTrack(vector<string>& arr, int idx, string& result){

        int n = arr.size();

        if(idx>=n){
            
            set<char> st;
            
            for(int i=0; i<result.length(); i++){
                if(st.find(result[i])!=st.end()){
                    return 0;
                }
                st.insert(result[i]);
            }

            return result.length();
        }

        int pick = INT_MIN;
        
        string s = arr[idx];

        if(checkValidity(s, result)){
            string temp = result;
            result += s;
            pick = backTrack(arr, idx+1, result);
            result = temp;
        }

        int notPick = backTrack(arr, idx+1, result);

        return max(pick, notPick);
    }

    int maxLength(vector<string>& arr) {
        
        string result = "";
        return backTrack(arr, 0, result);
    }
};
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