<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
{
    int helper(string &s)
    {
        stack<char> s1;
        int count = 0;
        for (auto &it : s)
        {
            if (it == ')')
            {
                while (!s1.empty() && s1.top() != '(')
                {
                    s1.pop();
                }
                if (s1.size() == 0)
                {
                    count++;
                }
                else
                {
                    s1.pop();
                }
            }
            else
            {
                s1.push(it);
            }
        }

        while (!s1.empty())
        {
            if (s1.top() == '(')
            {
                count++;
            }
            s1.pop();
        }

        return count;
    }

    bool check(string &s)
    {
        stack<char> s1;
        for (auto &it : s)
        {
            if (it == ')')
            {
                while (!s1.empty() && s1.top() != '(')
                {
                    s1.pop();
                }
                if (s1.size() == 0)
                {
                    return false;
                }
                else
                {
                    s1.pop();
                }
            }
            else
            {
                s1.push(it);
            }
        }
        while (!s1.empty() && s1.top() != '(')
        {
            s1.pop();
        }

        return s1.empty() == 1;
    }
    unordered_set<string> myset;
    int n;
    void func(string &s, int i, string &s2)
    {
        if (s2.length() == n)
        {
            if (check(s2))
            {
                myset.insert(s2);
            }
            return;
        }
        if(s2.size()>0 && s2[0]==')')
        {
            return;
        }
        if (s2.length() + s.length() - (i) < n)
        {
            return;
        }
        if(s[i]!=')' && s[i]!='(')
        {
            s2.push_back(s[i]);
            func(s, i + 1, s2);
            s2.pop_back();
        }
        else{
            func(s, i + 1, s2);
            s2.push_back(s[i]);
            func(s, i + 1, s2);
            s2.pop_back();
        }
        return;
    }

public:
    vector<string> removeInvalidParentheses(string s)
    {
        int a = helper(s);
        this->n = s.length() - a;
        string s3;
        func(s, 0, s3);
        vector<string> ans;
        for (auto &it : myset)
        {
            ans.push_back(it);
        }
        return ans;
    }
};
398229