<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> removeInvalidParentheses(string s) {
        int cnt = numberOfInvalidParam(s);
        vector<string> ans;
        set<string> st;
        map<string, int> map;
        solve(s, st, cnt, map);
        for (auto it : st) 
            ans.push_back(it);
        return ans;
    }
    int solve(string s, set<string>& st, int cnt, map<string, int>& map) {
        if (cnt == 0) {
            int a = numberOfInvalidParam(s);
            if (a == 0) 
                st.insert(s);
                return 1;
            return 0;
        }
        if (map.find(s) != map.end()) return map[s];

        for (int i=0; i<s.size(); i++) {
            string left = s.substr(0, i);
            string right = s.substr(i+1, s.size());
            map[left + right] = solve(left + right, st, cnt-1, map);
        }
        return map[s];
    }
    int numberOfInvalidParam(string s) {
        stack<int> st;
        for (int i=0; i<s.size(); i++) {
            if (s[i] == '(') st.push(s[i]);
            else if (s[i] == ')') {
                if (!st.empty() && st.top() == '(') st.pop();
                else st.push(s[i]);
            }
        }
        return st.size();
    }
};
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