<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 isUnique(string& s) {
        vector<int> v(26, 0);
        for (char c : s) {
            if (v[c - 'a']++ > 0) {
                return false;
            }
        }
        return true;
    }
    bool hasduplicate(string& s1, string& s2){
        vector<int> v(26);
        int n = s1.size();
        for(int i=0;i<n;i++){
            int diff = s1[i] - 'a';
            if(v[diff]>0){
                return true;
            }
            v[diff]++;
        }
        for(int i=0;i<s2.size();i++){
            int diff = s2[i] - 'a';
            if(v[diff]>0){
                return true;
            }
        }
        return false;
    }
    int solve(vector<string>& arr, int i , int n, string temp){
        if(i>=n){
            return temp.size();
        }
        int exc = solve(arr, i + 1, n, temp);
        int inc = 0;
        if (!hasduplicate(temp, arr[i]) && isUnique(arr[i])) {
            inc = solve(arr, i + 1, n, temp + arr[i]);
        }
        // int inc = 0;
        // int exc = 0;
        // if(hasduplicate(temp,arr[i])){
        //     // exclude
        //     exc = solve(arr,(i+1),n,temp);
        // }
        // else{
        //     inc = solve(arr,(i+1),n,temp) ;
        //     exc = solve(arr,(i+1),n,temp+arr[i]);
        // }
        return max(inc,exc);
    }
    int maxLength(vector<string>& arr) {
        string temp = "";
        int n = arr.size();
        int i = 0;
        return solve(arr,i,n,temp);

    }
};
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