<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:
    int getMinInvalid(string s) {
        stack<char> st;
        for (int i = 0; i < s.size(); i++) {
            if (s[i] == '(') {
                st.push('(');
            } else if (s[i] == ')') {
                if (!st.empty() && st.top() == '(') {
                    st.pop();
                } else {
                    st.push(')');
                }
            }
        }
        return st.size();
    }

    void invParen(string s, int start, int n, unordered_set<string>& result) {
        if (n == 0) {
            if (getMinInvalid(s) == 0) {
                result.insert(s);
            }
            return;
        }

        for (int i = start; i < s.size(); i++) {
            // if (i != start && s[i] == s[i - 1])
            //     continue; // To avoid duplicates
            if (s[i] == '(' || s[i] == ')') {
                string temp = s.substr(0, i) + s.substr(i + 1);
                invParen(temp, i, n - 1, result);
            }
        }
    }

    vector<string> removeInvalidParentheses(string s) {
        int n = getMinInvalid(s);
        unordered_set<string> result;
        invParen(s, 0, n, result);
        return vector<string>(result.begin(), result.end());
    }
};

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