<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> ans;
    map<string,bool> dp;
    bool isValid(string s){
        if(!s.size()) return false;
        stack<char> st;
        for(int i=0;i<s.size();i++){
            if(s[i]=='('){
                st.push(s[i]);
            }
            else if(s[i]==')'){
                if(st.empty()) return false;
                if(!st.empty()){
                    st.pop();
                }
            }
        }
        if(st.empty()) return true;
        return false;
    }
    void solve(string s){
        if(dp[s]) return;
        dp[s]=true;
        if(isValid(s)){
            ans.push_back(s);
            return;
        }
        for(int i=0;i<s.size();i++){
            if(s[i]=='(' or s[i]==')'){
                solve(s.substr(0,i)+s.substr(i+1));
            }
        }
    }
    vector<string> removeInvalidParentheses(string s) {
        solve(s);
        int sz=0;
        for(auto a:ans){
            int x=a.size();
            sz=max(sz,x);
        }
        vector<string> res;
        for(auto a:ans){
            if(a.size()==sz){
                res.push_back(a);
            }
        }
        sort(res.begin(),res.end());
        vector<string> result;
        if(!res.empty()){
            result.push_back(res[0]);
        }
        for(int i=1;i<res.size();i++){
            if(res[i]!=res[i-1]){
                result.push_back(res[i]);
            }
        }
        if(!result.size()) return {""};
        return result;
    }
};
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