<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:
    unordered_set<string> set;
    vector<string> ans;
    int len;

    bool isValid(string str){
        stack<char> st;
        for(int i = 0; i < str.length(); i++){
            if(str[i] == '('){
                st.push(str[i]);
            }
            else if(str[i] == ')'){
                if(!st.empty() and st.top() == '('){
                    st.pop();
                }
                else{
                    return false;
                }
            }
        }

        if(st.size() >= 1){
            return false;
        }
        return true;
    }

    void solve(string& s, string& str, int idx, int count){
        if(str.length() == len - count){
            if(isValid(str)){
                set.insert(str);
            }
            return;
        }

        if(idx >= s.length()){
            return;
        }

        str.push_back(s[idx]);
        solve(s, str, idx+1, count);
        str.pop_back();
        solve(s, str, idx+1, count);
    }

    vector<string> removeInvalidParentheses(string s) {
        len = s.length();
        int count = 0;
        stack<char>st;
        for(int i = 0; i < len; i++){
            if(s[i] == '('){
                st.push(s[i]);
            }
            else if(s[i] == ')'){
                if(!st.empty() and st.top() == '('){
                    st.pop();
                }
                else{
                    count++;
                }
            }
        }
        count += st.size();

        string str = "";
        solve(s, str, 0, count);

        for(auto x : set){
            ans.push_back(x);
        }

        return ans;
    }
};
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