<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) {
        if (s.size() == 1) return {s == "(" || s == ")" ? "": s};
        int leftCount = 0, removeRight = 0, removeLeft = 0;
        for (int i = 0; i < s.size(); i++) {
            if (s[i] == '(') {
                leftCount++;
            } else if (s[i] == ')') {
                leftCount--;
            }
            if (leftCount < 0) {
                removeRight++;
                leftCount = 0;
            }
        }
        removeLeft = leftCount;
        // cout << removeRight << " " << removeLeft << endl;
        string curStr = "";
        unordered_set<string> res;
        dfs(res, s, curStr, 0, 0, removeLeft, removeRight);
        return vector<string>(res.begin(), res.end());
    }
    void dfs(unordered_set<string>& res, string s, string& curStr, int idx, int leftCount, int removeLeft, int removeRight) {
        if (idx == s.size()) {
            // cout << curStr << " " << idx << " " << leftCount << " " << removeLeft << " " << removeRight << endl;
            if (leftCount == 0 && removeLeft == 0 && removeRight == 0) {
                res.insert(curStr);
            }
            return;
        }
        if (s.size() - idx < leftCount) return;
        char curChar = s[idx];
        if (curChar == '(') {
            curStr.push_back('(');
            dfs(res, s, curStr, idx + 1, leftCount + 1, removeLeft, removeRight);
            curStr.pop_back();
            if (removeLeft > 0) {
                // cout << curStr << " " << idx << " " << endl;
                dfs(res, s, curStr, idx + 1, leftCount, removeLeft - 1, removeRight);
            }
        } else if (curChar == ')') {
            if (leftCount > 0) {
                curStr.push_back(')');
                dfs(res, s, curStr, idx + 1, leftCount - 1, removeLeft, removeRight);
                curStr.pop_back();
            } 
            dfs(res, s, curStr, idx + 1, leftCount, removeLeft, removeRight - 1);
        } else {
            curStr.push_back(curChar);
            // cout << curStr << endl;
            dfs(res, s, curStr, idx + 1, leftCount, removeLeft, removeRight);
            curStr.pop_back();
        }
    } 
};
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