<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) {
        int removeCount = checkoutInvalid(s);
        DFS(s, removeCount, s, 0);
        return vector<string>(ans.begin(), ans.end());
    }
private:
    set<string> ans;
    int checkoutInvalid(string s) {
        int count = 0;
        stack<char> st;
        for(auto each : s) {
            if(each == '(') st.push(each);
            else if(each == ')') {
                if(st.empty()) {
                    count++;
                    continue;
                }
                st.pop();
            }
        }
        return st.size() + count;
    }
    void DFS(string &s, int removeCount, string crtS, int startIdx) {
        if(removeCount == 0) {
            if(ans.find(crtS) == ans.end() && checkoutInvalid(crtS) == 0) ans.insert(crtS);
            return;
        }
        for(int i = startIdx; i < crtS.size(); i++) {
            int originS = crtS[i];
            if(originS != '(' && originS != ')') continue;
            crtS.erase(crtS.begin() + i);
            DFS(s, removeCount-1, crtS, i);
            crtS.insert(crtS.begin() + i, originS);
        }
    }
};
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