<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:
    std::vector<std::string> removeInvalidParentheses(std::string s) {
        GenerateParentheses(s, "", 0);

        std::vector<std::string> res;
        for (auto str : map.begin()->second) {
            res.push_back(std::move(str));
        }

        return res;
    }

private:
    void GenerateParentheses(const std::string &s, std::string cur_str, int32_t idx) {
        while (idx < s.size() && isalpha(s[idx])) {
            cur_str += s[idx++];
        }

        if (IsValidParentheses(cur_str)) {
            map[cur_str.size()].insert(cur_str);
        }

        if (idx >= s.size()) return;
        GenerateParentheses(s, cur_str + s[idx], idx + 1);
        GenerateParentheses(s, cur_str, idx + 1);
    }

    bool IsValidParentheses(const std::string &s) {
        int p_cnt = 0;

        for (auto let : s) {
            if (let == '(') ++p_cnt;

            if (let == ')') {
                if (p_cnt <= 0) return false;
                --p_cnt;
            }
        }

        return p_cnt == 0;
    }

    std::map<int, std::unordered_set<std::string>, std::greater<>> map;
};
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