<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> removeInvalidParentheses(string s) {
        set<string> ans;
        int max = 0;
        helper(0, s, "", ans, max, 0);
        vector<string> vec;
        for (auto it : ans) vec.push_back(it);
        ans.clear();
        return vec;
    }
    void helper(int i, string& s, string temp, set<string>& ans, int& max, int open) {
        if (i == s.size()) {
            if (isValid(temp)) {
                if (temp.size() > max) {
                    max = temp.size();
                    ans.clear();
                    ans.insert(temp);
                } else if (temp.size() == max) ans.insert(temp);
                return;
            }
            return;
        }
        if(open > s.size()/2) return;

        if (s[i] != '(' && s[i] != ')') {
            temp += s[i];
            helper(i + 1, s, temp, ans, max, open);
        } else {
            if(open<=0 && s[i]==')'){
                helper(i + 1, s, temp, ans, max, open);
            }
            else{
                temp += s[i];
                if(s[i]=='(') open++;
                else open--;
                helper(i + 1, s, temp, ans, max, open);
                temp.erase(temp.size() - 1);
                if(s[i]=='(') open--;
                else open++;
                helper(i + 1, s, temp, ans, max, open);
            }
        }
    }
    bool isValid(string& s) {
        int balance = 0;
        for (char ch : s) {
            if (ch == '(') balance++;
            if (ch == ')') balance--;
            if (balance < 0) return false;
        }
        return balance == 0;
    }
};
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