<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:
    int isValid(string s)
    {
        stack<char> st;
        for(int i = 0;i < s.size();i++)
        {
            if(s[i] != '(' && s[i] != ')')
            continue;
            if(s[i] == '(')
            st.push('(');
            else
            {
                if(st.empty() || st.top() == ')')
                st.push(')');
                else
                st.pop();
            }
        }

        return st.size();
    }
    void solve(int i, int removes, string &output, set<string> &ans, string &s, int maxremoval)
    {
        if(i == s.size())
        {
            if(removes == maxremoval && !isValid(output))
            ans.insert(output);

            return;
        }
        if(removes > maxremoval)
        return;

        if(s[i] != '(' && s[i] != ')')
        {
            output.push_back(s[i]);
            solve(i + 1, removes, output, ans, s, maxremoval);
            output.pop_back();
        }
        else
        {
            output.push_back(s[i]);
            solve(i + 1, removes, output, ans, s, maxremoval);
            output.pop_back();

            solve(i + 1, removes + 1, output, ans, s, maxremoval);
        }
    }
    vector<string> removeInvalidParentheses(string s) 
    {
        int maxremoval = isValid(s);
        set<string> ans2;
        vector<string> ans;
        string output;
        
        solve(0, 0, output, ans2, s, maxremoval);

        for(auto it:ans2)
        ans.push_back(it);

        return ans;
    }
};
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