<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:
    bool isValid(string &s){
        stack<char> st;
        for(int i=0;i<s.size();i++){
            if(s[i] == ')'){
                if(!st.empty() && st.top() == '(')
                    st.pop();
                else
                    return 0;                
            }
            else if(s[i] == '(')
                st.push(s[i]);
        }
        return (st.size() >= 1) ? 0:1;
    }
    void solve(unordered_set<string> &ans, string &cur, int n, int idx, string &s){
        if(cur.size() == n){
            if(ans.find(cur) == ans.end()){
                if(isValid(cur))
                    ans.insert(cur);
            }
            return;
        }
        if(idx == s.size()) return; 
        cur+=s[idx]       ;
        solve(ans, cur, n, idx+1, s);
        cur.pop_back();
        solve(ans, cur, n, idx+1, s);
    }
    vector<string> removeInvalidParentheses(string s) {
        stack<char> st;
        int ct=0;
        string str = "";
        for(int i=0;i<s.size();i++){            
            if(s[i] == ')'){
                while(!st.empty() && st.top() != '(')
                    st.pop();
                if(!st.empty())
                    st.pop();
                else
                    ct++;
            }
            else if(s[i] == '(')
                st.push(s[i]);
        }      
        unordered_set<string> ans; 
        int x=0;             
        solve(ans, str, s.size()-st.size()-ct, x, s);
        vector<string> ret(ans.begin(), ans.end());
        if(!ret.size()) return{""};
        return ret;
    }
};
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