<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:
    void solveRec(int ind, string &s, string temp,set<string> &ans){
        if(ind == s.length()){
            int cnt = 0,len = temp.length();
            for(int i = 0;i < len;i++){
                if(temp[i] == '(')
                    cnt++;
                else if(temp[i] == ')' && cnt > 0)
                    cnt--; 
                else if(temp[i] == ')')
                    return;
            }
            if(cnt == 0)
                ans.insert(temp);
            return;
        }

        if(s[ind] == '(' || s[ind] == ')'){
            solveRec(ind + 1,s,temp,ans);
        }
        temp.push_back(s[ind]);
        int cnt = 0, len = temp.size();
        for(int i = 0;i < len;i++){
            if(temp[i] == '(')
                cnt++;
            else if(temp[i] == ')' && cnt > 0)
                cnt--; 
            else if(temp[i] == ')')
                return;
        }

        if(cnt < 0 || cnt > s.length()/2)
            return;
        solveRec(ind + 1,s,temp,ans);
       
    }
    vector<string> removeInvalidParentheses(string s) {
        set<string> ans;
        solveRec(0,s,"",ans);
        int maxLen = 0;
        for(auto it: ans){
            int len = it.length();
            maxLen = max(maxLen ,len);
        }
        vector<string> finalAns;
        for(auto it: ans){
            if(it.length() == maxLen)
                finalAns.push_back(it);
        }
        return finalAns;   
    }
};
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