<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>

"""
Approch

Brute use a set to track if repeating or not simple recursion

Optimal
Use bit manipulation since at max all 26 chars can be present and recursion 

TC : O(L * 2^n)
SC : O(n + 2^n)


"""

class Solution:
    def maxLength(self, arr: List[str]) -> int:

        n = len(arr)

        def get_bit_value(s):

            bit_val = 0

            for char in s:

                bit_pos = ord(char) - ord('a')

                if (bit_val >> bit_pos)  & 1:
                    # char repeating
                    return -1
                
                bit_val |= (1 << bit_pos)

            return bit_val

        memo = {}
        def solve(index, bit_value):

            if index == n:
                return 0
            
            if (index, bit_value) in memo:
                return memo[(index, bit_value)]
            
            curr_bit_val = get_bit_value(arr[index])
            include_length = 0

            if curr_bit_val != -1 and (curr_bit_val) & bit_value == 0:
                include_length = len(arr[index]) + solve(index+1, curr_bit_val | bit_value)
            
            # not include characters at this index
            not_include_length = solve(index+1, bit_value)
            memo[(index, bit_value)] =  max(include_length, not_include_length)
            return memo[(index, bit_value)]
            
        
        
        return solve(0, 0)
                

    """

        Set based approach


        maxSLen = 0

        n = len(arr)-1

        def maxLengthUtil(index,s):

            nonlocal maxSLen

            if index > n:

                return
            
            temp1 = s.copy()
            # take currString if  and not in s
            boolean = True
            for char in arr[index]:

                if char in temp1:

                    boolean = False

                    break

                temp1.add(char)
            
            if boolean:

                # take
                maxSLen = max(maxSLen,len(temp1))

                maxLengthUtil(index+1,temp1)
            
            # not tale

            maxLengthUtil(index+1,s)

        s = set()

        maxLengthUtil(0,s)

        return maxSLen
    """




        
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