<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>

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
static const int _ = []() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr); return 0; }();

class Solution {
public:
    vector<string> removeInvalidParentheses(string s) {
        int n = s.size();
        int N = 0;
        for(int i = 0; i < n; i++) {
            if(s[i] == '(' or s[i] == ')') {
                N++;
            }
        }     


        auto valid = [](string& str) {
            stack<char> st;
            for(int i = 0; i < str.size(); i++) {
                if(str[i] >= 'a' and str[i] <= 'z') {
                    continue;
                }
               if(str[i] == '(') {
                st.push(str[i]);
               }
               else {
                if(st.empty()) {
                    return false;
                }
                else {
                    st.pop();
                }
               }
            }
            return (st.size() == 0);
        };

        int maxi = 0;

        int M = (1 << N);

        unordered_set<string> ans;

        for(int i = 0; i < M; i++) {
            string st;
            int x = 0 , y = 0;
            int ptr = 0;
            for(int j = 0; j < s.size(); j++) {
                if(s[j] >= 'a' and s[j] <= 'z') {
                    st += s[j];
                    continue;
                }
                if(((i >> ptr) & 1) == 1) {
                    st += s[j];
                    if(st.back() == '(') x++;
                    else y++;
                }
                ptr++;
            }
            if(x == y and valid(st) and st.size() >= maxi) {
                int cur = st.size();
                if(cur > maxi) {
                    maxi = cur;
                    ans.clear();
                }
                ans.insert(st);
            }
        }
        
        return vector<string> (ans.begin() , ans.end());
    }
};
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