<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 minRemoval = 0;
    unordered_map <string, bool> isExist;

    void handle(string s, int i, int n, string curStr, int curSum) {
        if (i == n) {
            if (curSum == 0 && curStr.size() + minRemoval == n) {
                if (!isExist[curStr]) {
                    isExist[curStr] = true;
                    ans.push_back(curStr);
                }
            }
            return;
        }

        if (s[i] == ')') {
            if (curSum - 1 >= 0 && curStr.size() + 1 <= n - minRemoval) {
                handle(s, i + 1, n, curStr + s[i], curSum - 1);
            }
            if (curStr.size() + minRemoval + (n - i) >= n) {
                handle(s, i + 1, n, curStr, curSum);
            }
        } else if (s[i] == '(') {
            if (curStr.size() + 1 <= n - minRemoval) {
                handle(s, i + 1, n, curStr + s[i], curSum + 1);
            }
            
            if (curStr.size() + minRemoval + (n - i) >= n) {
                handle(s, i + 1, n, curStr, curSum);
            }
        } else {
            handle(s, i + 1, n, curStr + s[i], curSum);
        }
    }

    vector<string> removeInvalidParentheses(string s) {
        int curSum = 0;
        for (int i = 0; i < s.size(); ++i) {
            if (s[i] == '(') {
                curSum++;
            } else if (s[i] == ')') {
                curSum--;
            }

            if (curSum < 0) {
                minRemoval++;
                curSum++;
            }
        }
        minRemoval += curSum;

        handle(s, 0, s.size(), "", 0);
        return ans;   
    }
};
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