<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 {
public:
    vector<string> removeInvalidParentheses(string s) {
        vector<pair<string, int>> res;
        res.push_back({"",0});
        for (int i = 0; i < s.size(); ++i)
        {
            vector<pair<string, int>> newp;
            for (auto& p : res )
            {
                if ('a' <= s[i] && s[i] <= 'z')
                    p.first.push_back(s[i]);
                else {
                    if (s[i] == ')' && p.second > 0)
                        newp.push_back( { p.first + ')', p.second-1 } );
                
                    else if (s[i] == '(')
                        newp.push_back( { p.first + '(', p.second+1 } );
                }
            }
            for (auto& p : newp)
                res.push_back(p);
        }

        int mostlong = 0;
        for (auto& p : res)
            if (mostlong < p.first.size() && p.second == 0) mostlong = p.first.size();
        
        set<string> out;
        for (auto& p : res)
            if (p.first.size() == mostlong && p.second == 0)
                out.insert(p.first);

        vector<string> outt;
        for (auto& p : out) outt.push_back(p);
        return outt;
    }
};
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