<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 {
private:
    string str;

    bool isValid(int removedIndices){
        int leftCtr = 0;
        for (int i = 0; i < str.length(); ++i){
            if ((1 << i) & removedIndices){
                continue;
            }
            if (str[i] == '('){
                ++leftCtr;
            }
            else if (str[i] == ')'){
                if (leftCtr == 0){
                    return false;
                }
                --leftCtr;
            }
        }
        return leftCtr == 0;
    }

    string build(int removedIndices){
        string res;
        for (int i = 0; i < str.length(); ++i){
            if ((1 << i) & removedIndices){
                continue;
            }
            res += str[i];
        }
        return res;
    }

public:
    vector<string> removeInvalidParentheses(const string &s) {
        str = s;
        queue<int> q;
        q.push(0);
        int maxLen;
        unordered_set<string> res;
        while (!q.empty()){
            int removedIndices = q.front();
            q.pop();
            string thisStr = build(removedIndices);
            if (!res.empty() && thisStr.length() < maxLen){
                break;
            }
            if (isValid(removedIndices)){
                if (res.empty()){
                    maxLen = thisStr.size();
                }
                res.insert(thisStr);
                if (thisStr == ""){
                    break;
                }
                continue;
            }
            for (int i = str.length() - 1; i >= 0 && !((1 << i) & removedIndices); --i){
                if (str[i] != '(' && str[i] != ')'){ continue; }
                q.push(removedIndices | (1 << i));
            }
        }
        return vector<string>(res.begin(), res.end());
    }
};
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