<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 checkforbalancedParanthesis(string str){
        stack<char>st;
        for(int i=0;i<str.size();i++){
            if(str[i]=='('){
                st.push(str[i]);
            }
            else if(str[i]==')'){
                if(st.size()!=0 && st.top()=='(') st.pop();
                else st.push(')');
            }
        }
      return st.size();
    }
    void removeInvalidParenthesis(string s,unordered_map<string,bool>&visited,int remove,vector<string>&ans){
        if(visited[s]) return;
        visited[s]=true;
        if(remove==0){
            int valid=checkforbalancedParanthesis(s);
            if(valid==0){
               ans.push_back(s);
            }
        }

        for(int i=0;i<s.size();i++){
            string leftstr=s.substr(0,i);
            string rightstr=s.substr(i+1);
            string newstr=leftstr+rightstr;
            removeInvalidParenthesis(newstr,visited,remove-1,ans);
        }
    }
    vector<string> removeInvalidParentheses(string s) {
        unordered_map<string,bool>visited;
        int remove=checkforbalancedParanthesis(s);
        vector<string>ans;
        removeInvalidParenthesis(s,visited,remove,ans);
        return ans;


    }
};
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