<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:
    // basic dp problem
    bool checkunike(string t){
        unordered_map<int,int>freq;
        for(int i=0;i<t.length();i++){
            freq[t[i]]++;
            if(freq[t[i]] >1){
                return false;
            }
        
        }
        return true;
    }
    bool checkunique(string a, string b) {
        unordered_map<char, bool> vis;
        for (int i = 0; i < a.length(); i++) {
            vis[a[i]] = true;
        }
        for (int i = 0; i < b.length(); i++) {
            if (vis[b[i]]) {
                return false;
            }
        }
        return true;
    }
    int dp(vector<string>& arr, string temp, int i, int& n) {
        if (i >= n) {
            return 0;
        }
        // we have two cases
        int take = 0;
        int nottake = 0;
        if (checkunike(arr[i]) &&checkunique(arr[i], temp)) {
            take += arr[i].length() + dp(arr, temp + arr[i], i + 1, n);
        }
        nottake = dp(arr, temp, i + 1, n);

        return max(take, nottake);
    }
    int maxLength(vector<string>& arr) {
        int n = arr.size();
        return dp(arr, "", 0, n);
    }
};
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