<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 solve(string str, int mra, set<string>&st, map<string,bool>&mp)
{
    if(mra==0)
    {
        int mrnow=getMinRemovals(str);
        if(mrnow==0)
        {
            st.insert(str);
            return;
        }
    }
    if(mp[str]) return;
    mp[str]=true;
    for(int i=0;i<str.size();i++)
    {
        string left=str.substr(0,i);
        string right=str.substr(i+1);
        solve(left+right,mra-1,st,mp);
    }
}

int getMinRemovals(string str)
{
    stack<char>st;
    for(int i=0;i<str.size();i++)
    {
        if(!st.empty() && st.top()=='(' && str[i]==')')
        {
            st.pop();
        }
        else if(str[i]=='(' || str[i]==')')
        {
            st.push(str[i]);
        }
    }
    return st.size();
}

    vector<string> removeInvalidParentheses(string str) {
        int mra=getMinRemovals(str);
        set<string>st;
        map<string,bool>mp;
        solve(str,mra,st,mp);
        vector<string>ans(st.begin(),st.end());
        return ans;
    }
};
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