<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:
        def valid(s):
            set_ = set(list(s))
            return len(set_) == len(s)
        arr = [''.join(sorted(x)) for x in arr if valid(x)]
        arr = list(set(arr))
        visited = {}
        def dfs(curr, arr):
            if arr == []:
                return len(curr)
            if (curr, arr[0]) in visited:
                return visited[(curr, arr[0])]
            res = len(curr)
            for i in range(len(arr)):
                x = arr[i]
                if valid(curr + x):
                    res = max(res, max(dfs(curr+x, arr[i+1::]), dfs(curr, arr[i+1::])))
                else:
                    res = max(res, dfs(curr, arr[i+1::]))
            visited[(curr, arr[0])] = res
            return res
        return dfs("", arr)


        # return 0
        
        # res = 0
        # n = len(arr)
        # start = 0
        # i = 0
        # curr = ""
        # while i < n:
        #     curr += arr[i]
        #     if valid(curr):
        #         res = max(res, len(curr))
        #         i += 1
        #     else:
        #         while not valid(curr):
        #             print(curr)
        #             curr = curr[len(arr[start])::]
        #             start += 1
        #             res = max(res, len(curr))
        #             print(curr)
        #             print("##########")
        #         i += 1
        # return res


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