<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:
set<string> globalSet;
string s;
string cur;
int balance=0;

void dfs(int i)
{
    if(balance<0) return;
    // cout<<cur<<endl;

    if(i>=s.size())
    {
        // cout<<i<<endl;
        // cout<<balance<<" "<<cur<<" "<<globalSet.size()<<" "<<*globalSet.begin()<<endl;
        if(balance==0 && cur.size()>0)
        {
            if(globalSet.size()!=0)
            {
                {
                    auto tempstr=*globalSet.begin();

                    if(tempstr.size()<cur.size())
                    {
                        // cout<<balance<<" "<<cur<<" "<<globalSet.size()<<" "<<*globalSet.begin()<<" "<<88<<endl;
                        globalSet.clear();
                        globalSet.insert(cur);
                    }
                    else if(tempstr.size()==cur.size())
                    {
                        // cout<<balance<<" "<<cur<<" "<<globalSet.size()<<" "<<99<<endl;
                        globalSet.insert(cur);
                    }
                }
            }
            else
            {
                // cout<<balance<<" "<<cur<<" "<<globalSet.size()<<endl;
                globalSet.insert(cur);
            }
        }
        return;
    }

    if(s[i]!='(' && s[i]!=')' && balance>=0)
    {
        cur.push_back(s[i]);
        dfs(i+1);
        cur.pop_back();
    }
    else if(s[i]=='(' && balance>=0)
    {
        balance++;
        cur.push_back(s[i]);
        dfs(i+1);
        cur.pop_back();
        balance--;
    }
    else if(s[i]==')' && balance>=1)
    {
        balance--;
        cur.push_back(s[i]);
        dfs(i+1);
        cur.pop_back();
        balance++;
    }
    dfs(i+1);
}

    vector<string> removeInvalidParentheses(string str) {
        s=str;
        dfs(0);

        vector<string> ans;

        for(auto it=globalSet.begin();it!=globalSet.end();it++)
        {
            ans.push_back(*it);
        }

        if(ans.size()==0) ans.push_back("");

        return ans;
    }
};
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