<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 {
    unordered_set<string>st;
    int mini=0;
    void solve(int ind,string temp,string &s,int d,int x){
        if(d<0)return;
        if(ind==s.size()){
            if(x==0)st.insert(temp);
            return;
        }
        if(s[ind]!='('&&s[ind]!=')'){
            solve(ind+1,temp+s[ind],s,d,x);
            return;
        }
        if(s[ind]==')'&&x==0){

        }else{
            int y=x;
            if(s[ind]=='(')y++;
            else y--;
            solve(ind+1,temp+s[ind],s,d,y);
        }
        solve(ind+1,temp,s,d-1,x);
    }
public:
    vector<string> removeInvalidParentheses(string &s) {
        int x=0;
        for(char c:s){
            if(c=='(')x++;
            else if(c==')'){
                if(x>0)x--;
                else mini++;
            }
        }
        mini+=x;
        string temp;
        solve(0,temp,s,mini,0);
        vector<string>ans(st.begin(),st.end());
        return ans;
    }
};
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