<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 {
private:
    int getRemoval(string &s){

    stack<char>st;

    for(char& ch: s){
        if(ch == '('){
            st.push(ch);
        }
        else if(ch == ')'){
            if(st.empty() || st.top() == ')'){
                st.push(ch);
            }
            else if(st.top()=='('){
                st.pop();
            }
        }
    }
    return st.size();
}

void getString(string s, int minRemoval, unordered_set<string>& st, unordered_set<string>& visited){

    if(visited.count(s)) return;
    visited.insert(s);

    if(minRemoval==0){
        int minRemoveNow = getRemoval(s);
        if(minRemoveNow==0){
            st.insert(s);
        }
        return;
    }


    for (int i = 0; i < s.length(); i++)
    {
        string left = s.substr(0, i);
        string right = s.substr(i+1);

        getString(left+right, minRemoval-1, st, visited);
    }
    
}
public:
    vector<string> removeInvalidParentheses(string s) {
        int n = s.length();

        int minRemoval = getRemoval(s);

        unordered_set<string>st;

        unordered_set<string>visited;

        getString(s, minRemoval, st, visited);
        vector<string>vec(st.begin(), st.end());
        return vec;
    }
};
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