<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:

    // Can also be solved using bit manipulation

    unordered_set<char>st;

    unordered_map<string,int>mp;

    bool canTake(string a, string b){

        st.clear();

        for(int i=0; i<a.length(); i++){
            st.insert(a[i]);
        }

        for(int i=0; i<b.size(); i++){

            if( st.find(b[i]) != st.end() ) return false;
        }

        return true;
    }

    bool allCharUnique(string &s){

        st.clear();
        for(int i=0; i<s.length(); i++){
            st.insert(s[i]);
        }

        if(st.size() == s.length()) return true;
        return false;
    }

    int solve(int i, vector<string>&arr, int n, string &ans){

        if(i>=n) {
            return 0;
        }

        if(mp.find(ans) != mp.end()) return mp[ans]; 
 
        int taken = 0;
        if( (ans.length() == 0 || canTake(ans, arr[i])) && allCharUnique(arr[i])){
            
            int len = arr[i].length();
            
            ans = ans+arr[i];

            taken = arr[i].length() + solve(i+1, arr, n, ans);

            for(int k=0; k<len; k++){
                ans.pop_back();
            }
        }

        int skipped = solve(i+1, arr, n, ans);

        return mp[ans] = max(taken, skipped);

    }

    int maxLength(vector<string>& arr) {
        
        int n = arr.size();
        if(n==1){

            bool flag = allCharUnique(arr[0]);
            if(flag) return arr[0].length();
            return 0;
        }

        string ans = "";

        return solve(0,arr,n, ans);
    }
};
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