<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) {
        unordered_set<string> result;
        int left_removed = 0;
        int right_removed = 0;
        for(auto c : s) {
            if(c == '(') {
                ++left_removed;
            }
            if(c == ')') {
                if(left_removed != 0) {
                    --left_removed;
                }
                else {
                    ++right_removed;
                }
            }
        }
        helper(s, 0, left_removed, right_removed, 0, "", result);
        return vector<string>(result.begin(), result.end());
    }
private:
    void helper(string s, int index, int left_removed, int right_removed, int pair, string path, unordered_set<string>& result) {
        if(left_removed + right_removed > s.length() - index)
            return;
        if(index == s.size()) {
            if(left_removed == 0 && right_removed == 0 && pair == 0) {
                result.insert(path);
            }
            return;
        }
        if(s[index] != '(' && s[index] != ')') {
            helper(s, index + 1, left_removed, right_removed, pair, path + s[index], result);
        }
        else {
            if(s[index] == '(') {
                if(left_removed > 0) {
                    helper(s, index + 1, left_removed - 1, right_removed, pair, path, result);
                }
                helper(s, index + 1, left_removed, right_removed, pair + 1, path + s[index], result);
            }
            if(s[index] == ')') {
                if(right_removed > 0) {
                    helper(s, index + 1, left_removed, right_removed - 1, pair, path, result);
                }
                if(pair > 0) {
                    helper(s, index + 1, left_removed, right_removed, pair - 1, path + s[index], result);
                }
            }
        }
    }
};
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