<p>Given a string <code>s</code> that contains parentheses and letters, remove the minimum number of invalid parentheses to make the input string valid.</p>

<p>Return <em>a list of <strong>unique strings</strong> that are valid with the minimum number of removals</em>. You may return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;()())()&quot;
<strong>Output:</strong> [&quot;(())()&quot;,&quot;()()()&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;(a)())()&quot;
<strong>Output:</strong> [&quot;(a())()&quot;,&quot;(a)()()&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;)(&quot;
<strong>Output:</strong> [&quot;&quot;]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 25</code></li>
	<li><code>s</code> consists of lowercase English letters and parentheses <code>&#39;(&#39;</code> and <code>&#39;)&#39;</code>.</li>
	<li>There will be at most <code>20</code> parentheses in <code>s</code>.</li>
</ul>

class Solution:
    def removeInvalidParentheses(self, s: str) -> List[str]:
        self.longeststring = -1
        self.res = set()

        self.dfs(s,0,[],0,0)

        return self.res
    
    def dfs(self, string, cur_index, cur_res, lcount, rcount):
        if cur_index >= len(string):
            if lcount == rcount:
                if len(cur_res) > self.longeststring:
                    self.longeststring = len(cur_res)

                    self.res = set()
                    self.res.add("".join(cur_res))
                elif len(cur_res) == self.longeststring:
                    self.res.add("".join(cur_res))
        else:
            cur_char = string[cur_index]

            if cur_char == "(":
                cur_res.append(cur_char)
                self.dfs(string, cur_index+1, cur_res, lcount + 1, rcount)
                cur_res.pop()
                self.dfs(string, cur_index+1, cur_res, lcount, rcount)
            elif cur_char == ")":
                self.dfs(string, cur_index+1, cur_res, lcount, rcount)

                if lcount > rcount:
                    cur_res.append(cur_char)
                    self.dfs(string, cur_index+1, cur_res, lcount, rcount+1)
                    cur_res.pop()
            else:
                cur_res.append(cur_char)
                self.dfs(string, cur_index+1, cur_res, lcount , rcount)
                cur_res.pop()

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