<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) {
        unordered_set<int> V;
        V.insert(0); // 0000

        for (int i = 0; i < presses; i++) {
            unordered_set<int> V2;
            for (int curr: V) {
                for (int j = 0; j < 4; j++) {
                    V2.insert(curr ^ (1<<j));
                }
            }
            V = V2;
        }

        set<vector<bool>> S;
        for(int curr:V){
            vector<bool> L(n, true);
            int b1 = curr & 1;
            if (b1 == 1) {
                for (int i = 0; i < n; i++) L[i] =!L[i];
            }
            int b2 = (curr >> 1) & 1;
            if (b2 == 1) {
                for (int i = 1; i < n; i+=2) L[i] = !L[i];
            }
            int b3 = (curr >> 2) & 1;
            if (b3 == 1) {
                for (int i = 0; i < n; i+=2) L[i] = !L[i];
            }
            int b4 = (curr >> 3) & 1;
            if (b4 == 1) {
                for (int i = 0; i < n; i+=3) L[i] = !L[i];
            }
            S.insert(L);
        }
        return S.size();
    }

};
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