<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 getMinInvalid(string s)
    {
        stack<char> st;
        int i=0;
        while(i<s.size())
        {
            if(s[i] == '(')
            {
                st.push(s[i]);
            }
            else if(s[i] == ')')
            {
                if(st.size() > 0 && st.top() == '(')
                    st.pop();
                else
                    st.push(')');
            }
            i++;
        }
        return st.size();
    }
    void solve(string s,int minInv,vector<string>& ans,unordered_map<string,int>& mp)
    {
        if(mp[s] != 0)
            return;
        else
            mp[s]++;
        if(minInv < 0)
            return;
        if(minInv == 0)
        {
            if(!getMinInvalid(s))
            {
                ans.push_back(s);
            }
            return;
        }
        for(int i=0;i<s.size();i++)
        {
            string left = s.substr(0,i);
            string right = s.substr(i+1);
            solve(left+right,minInv-1,ans,mp);
        }
    }
    vector<string> removeInvalidParentheses(string s) {
        vector<string> res;
        unordered_map<string,int> mp;
        solve(s,getMinInvalid(s),res,mp);
        return res;
    }
};
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