<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 backtrack(unordered_set<string>& ans, unordered_map<string, int>& mp2, string& s, string& o, int idx) {
    if (s.length() == idx)
        return;

    o.push_back(s[idx]);
    
    if (mp2[o] == 0) {
        solve(ans, o);
        backtrack(ans, mp2, s, o, idx + 1);
    }
    mp2[o]++;
    
    o.pop_back();
    
    if (mp2[o] == 0) {
        solve(ans, o);
        backtrack(ans, mp2, s, o, idx + 1);
    }
    mp2[o]++;
}

void solve(unordered_set<string>& ans, string& s) {
    int balance = 0;
    for (char i : s) {
        if (i == '(')
            balance++;
        else if (i == ')') {
            if (balance == 0)
                return;
            balance--;
        }
    }
    if (balance == 0 && !s.empty())
        ans.insert(s);
}

vector<string> removeInvalidParentheses(string s) {
    unordered_set<string> ans;
    unordered_map<string, int> mp2;
    string o;
    vector<string> x;
    backtrack(ans, mp2, s, o, 0);

    int mx = -1;
    for (const auto& i : ans) {
        int l = i.length();
        mx = max(mx, l);
    }

    for (const auto& i : ans) {
        if (i.length() == mx)
            x.push_back(i);
    }

    if (x.empty())
        return {""};
    return x;
}

};
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