<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 f(int i,int count,string temp,string &str,int &k,vector<string>&ans,set<pair<int,string>>&s,int&n){
        if(s.count({i,temp}))return;
        s.insert({i,temp});
        if(i>=n){
            cout<<temp<<" "<<count<<endl;
            if(count==0 && (n-temp.size())==k){
                ans.push_back(temp);
            }
            return;
        }
        
        if(str[i]=='('){
            f(i+1,count,temp,str,k,ans,s,n);
            f(i+1,count+1,temp+'(',str,k,ans,s,n);
        }else if(str[i]==')'){
            f(i+1,count,temp,str,k,ans,s,n);
            if(count>0){
                f(i+1,count-1,temp+')',str,k,ans,s,n);
            }
        }else{
            f(i+1,count,temp+str[i],str,k,ans,s,n);
        }
    }
    vector<string> removeInvalidParentheses(string s) {
        int k=0;
        int n=s.size();
        int count=0;
        for(int i=0;i<n;i++){
            if(s[i]=='('){
                count++;
            }else if(s[i]==')'){
                if(count>0){
                    count--;
                }else{
                    k++;
                }
            }
        }
        k+=count;
        vector<string>ans;
        set<pair<int,string>>st;
        f(0,0,"",s,k,ans,st,n);
        return ans;
    }
};
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