<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:
    void check(set<string>& result, const string& s, int pos, int open, int removals) {
        int len = s.length();
        // skip all non-brackets
        while (pos < len && s[pos] != '(' && s[pos] != ')') { 
            pos++;
        }
        if (pos == len) {
            // check if the string is valid
            if (open == 0) {
                // check number of removals
                if (removals <= min) {
                    min = removals;
                    // store the current string
                    result.insert(s);
                }
            }
            return;
        }
        // next check
        if (s[pos]=='(') {
            // try keeping opening bracket
            check(result, s, pos+1, open+1, removals);
            // try removing opening bracket
            if (removals < min) {
                string scopy(s);
                scopy.erase(pos,1);
                check(result, scopy, pos, open, removals+1);
            }
        } else {
            // process closing bracket
            if (open > 0) {
                // try keeping closing bracket
                check(result, s, pos+1, open-1, removals);
            }
            // check removal
            if (removals < min) {
                string scopy(s);
                scopy.erase(pos,1);
                check(result, scopy, pos, open, removals+1);
            }
        }
    }
    vector<string> removeInvalidParentheses(string s) {
        set<string> result;
        check(result, s, 0, 0, 0);
        return vector<string>(result.begin(), result.end());
    }

    int min{numeric_limits<int>::max()};
};
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