<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:
    vector <string> ans;
    int findrem(string s)
    {
        int n = s.size();
        stack <int> st;
        for(auto it : s)
        {
          if(it=='(') st.push('(');
          else if(it==')') 
          {
            if(!st.empty() && st.top()=='(') st.pop();
            else st.push(')');
          }
          else  continue;
        }

        return st.size();
    }
   void solve(string s,  unordered_map <string,bool> &mp, int rem)
    {
        int n = s.size();
        if(mp[s]) return;

        mp[s] = true;

        if(rem==0)
        {
            int vl = findrem(s);
            if(rem==vl)
            {
                ans.push_back(s);
            }

        }
        for(int i=0;i<n;i++)
        {
           string left = s.substr(0,i);
           string right = s.substr(i+1,n);
           string temp = left+right;
           solve(temp,mp,rem-1);
        }
    }
    vector<string> removeInvalidParentheses(string s) {
        
        int n = s.size();
        int rem = findrem(s);
        //cout<<rem;
        unordered_map <string,bool> mp;
        solve (s, mp,rem);
        return ans;
    }
};
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