<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:
    bool isValid(const string& s)
    {
        stack <char> sk;
        int slen = s.size();
        for (auto c : s)
        {
            if (c == ')')
            {
                if (sk.empty())
                    return false;
                else
                    sk.pop();
            }
            if (c == '(')
                sk.push(c);
        }
        if (sk.empty())
            return true;
        else
            return false;
    }
public:
    vector<string> removeInvalidParentheses(string s) {
        set<string> ans;
        if (isValid(s)) {
            return {s};
        }
        queue<string> que;
        que.push(s);
        bool flag = 1; // not found yet
        while (!que.empty() && flag)
        {
            int n = que.size();
            int slen = que.front().size();
            set<string> level;
            for (int i = 0; i < n; ++i)
            {
                for (int j = 0; j < slen; ++j)
                {
                    string curr = que.front();
                    if (j > 0 && curr[j] == curr[j - 1])
                        continue;
                    if (curr[j] == '(' || curr[j] == ')')
                    {
                        curr.erase(j, 1);
                        if (isValid(curr))
                        {
                            flag = 0;
                            ans.insert(curr);
                        }
                        else
                            level.insert(curr);
                    }
                }
                que.pop();
            }
            for (auto levelnum : level)
                que.push(levelnum);
        }
        vector <string> finalans;
        for (auto s : ans)
            finalans.push_back(s);
        return finalans;
    }
};
164998