<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:
    def maxLength(self, arr: List[str]) -> int:
        n = len(arr)
        blocked = {}
        letters = {}
        for i in range(n):
            x = letters.get(arr[i], set())
            for c in arr[i]:
                x.add(c)

            letters[arr[i]] = x       

        blocked[0] = set()
        for i in range(1, n):
            x = blocked[i-1].copy()
            x.add(i-1)
            blocked[i] = x

        for i in range(n-1):
            for j in range(i+1, n):
                a = letters[arr[i]]
                b = letters[arr[j]]
                common = False
                for c in a:
                    if c in b:
                        common = True
                        break

                if(common):
                    blocked[i].add(j)

        blacklisted = set()
        for i in range(n):
            if(not(len(list(arr[i]))==len(set(list(arr[i]))))):
                blacklisted.add(i)

        for i in range(n):
            blocked[i] = blocked[i].union(blacklisted)

        print(letters)
        print(blocked)

        def dfs(i, b1):
            ans = len(letters[arr[i]])
            b2 = blocked[i]
            x = b1.union(b2)
            for j in range(i+1, n):
                if j not in x:
                    ans = max(ans, len(letters[arr[i]]) + dfs(j, x.copy()))

            return ans

        res = 0
        for i in range(n):
            if i not in blacklisted:
                res = max(res, dfs(i, set()))


        return res

17100