<p>There is a room with <code>n</code> bulbs labeled from <code>1</code> to <code>n</code> that all are turned on initially, and <strong>four buttons</strong> on the wall. Each of the four buttons has a different functionality where:</p>

<ul>
	<li><strong>Button 1:</strong> Flips the status of all the bulbs.</li>
	<li><strong>Button 2:</strong> Flips the status of all the bulbs with even labels (i.e., <code>2, 4, ...</code>).</li>
	<li><strong>Button 3:</strong> Flips the status of all the bulbs with odd labels (i.e., <code>1, 3, ...</code>).</li>
	<li><strong>Button 4:</strong> Flips the status of all the bulbs with a label <code>j = 3k + 1</code> where <code>k = 0, 1, 2, ...</code> (i.e., <code>1, 4, 7, 10, ...</code>).</li>
</ul>

<p>You must make <strong>exactly</strong> <code>presses</code> button presses in total. For each press, you may pick <strong>any</strong> of the four buttons to press.</p>

<p>Given the two integers <code>n</code> and <code>presses</code>, return <em>the number of <strong>different possible statuses</strong> after performing all </em><code>presses</code><em> button presses</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1, presses = 1
<strong>Output:</strong> 2
<strong>Explanation:</strong> Status can be:
- [off] by pressing button 1
- [on] by pressing button 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, presses = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong> Status can be:
- [off, off] by pressing button 1
- [on, off] by pressing button 2
- [off, on] by pressing button 3
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 3, presses = 1
<strong>Output:</strong> 4
<strong>Explanation:</strong> Status can be:
- [off, off, off] by pressing button 1
- [off, on, off] by pressing button 2
- [on, off, on] by pressing button 3
- [off, on, on] by pressing button 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>0 &lt;= presses &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int flipLights(int n, int presses) {
        /*
            1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
            
            1: f1    f3 f4
            2: f1 f2
            3: f1    f3
            4: f1 f2    f4
            5: f1    f3
            6: f1 f2
            --------------
            7: f1    f3 f4
        */
        unordered_set<int> seen;
        queue<int> q;
        n = min(n, 6);
        int init = (1<<n)-1;
        q.push(init);
        int shift = max(0, 6-n);
        for(int i=0; i<presses; i++){
            int size = q.size();
            seen.clear();
            for(int t=0; t<size; t++){
                auto cur = q.front(); q.pop();

                unordered_set<int> cads;
                cads.insert(cur^(0b111111>>shift));
                cads.insert(cur^(0b101010>>shift));
                cads.insert(cur^(0b010101>>shift));
                cads.insert(cur^(0b100100>>shift));

                for(auto next: cads){
                    if(seen.count(next)) continue;

                    seen.insert(next);
                    q.push(next);
                }
            }
        }
        return q.size();
    }
};
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