<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.out = set()
        unabalancedRight = 0
        unbalancedLeft = 0
        for c in s:
            if c=='(': 
                unbalancedLeft+=1
            elif c==')':
                if unbalancedLeft>0: 
                    unbalancedLeft-=1
                else: unabalancedRight+=1
        self.generate(s, 0, unbalancedLeft, unabalancedRight)
        
        return self.out
        
    @cache
    def generate(self, s, start, unbalancedLeft, unabalancedRight):
        if unbalancedLeft==0 and unabalancedRight==0 and self.isValid(s):
            self.out.add(s)   

        i=start
        if unabalancedRight>0:
            while i<len(s):
                if s[i]==")":
                    self.generate(s[:i]+ s[i+1:], i, unbalancedLeft, unabalancedRight-1)
                i+=1
            
        while i<len(s):
            if s[i]=="(": 
                self.generate(s[:i]+ s[i+1:], i, unbalancedLeft-1, unabalancedRight)
            i+=1
    
    def isValid(self, s):
        ct = 0
        for c in s:
            if c=='(':
                ct+=1
            elif c==')':
                ct-=1
                if ct < 0:
                    return False
        return ct==0

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