<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:
    #timecomplexity 2^n*n**2
    #better apporach is bitwise operations because hash taking time
    def recur(self, arr, hashi, i, l):
        if i >= len(arr):
            return l
        
        maxi = l
        for j in range(i, len(arr)):
            flag = True
            new_hashi = hashi.copy()
            
            for k in arr[j]:
                if k in new_hashi and new_hashi[k] > 0:
                    flag = False
                    break
                else:
                    new_hashi[k] = 1
            
            if flag:
                maxi = max(maxi, self.recur(arr, new_hashi, j + 1, l + len(arr[j])))
        
        return maxi
    def bitwise(self,arr):
        dp = [(0,0)]
        maxi = 0
        for string in arr:
            bitwise = 0
            flag = True
            for char in string:
                bit  = 1<<(ord(char)-ord('a'))
                if(bitwise & bit):
                    flag = False
                    break
                bitwise|=bit
            if not flag:
                continue
            for mask,length in dp:
                if(mask & bitwise == 0):
                    dp.append(((mask|bitwise),length+len(string)))
                    maxi = max(maxi,length+len(string))
        return maxi

    def maxLength(self, arr: List[str]) -> int:
        return self.bitwise(arr)
        # return self.recur(arr, {}, 0, 0)

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