<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 17 18
//         1 x 3 x 5 x  7 x 9 x  11 x   13 x  15 x  17 x
//         x 2 x 4 x 6  x 8 x 10 x  12  x  14 x  16 x  18
//         x 2 3 x 5 6  x 8 9 x  11 13  x  14 15 x  17 18           
        
//         => if(n > 6) n = n%6 + 6
     
        
//         [s, e]d
//         n = s + (x-s)%d
        
        if(n > 6) n = n%6 + 6;
    
        // presses = 0
        unordered_set<int> s = {(1<<n) -1 };
        
        for(int i=1; i<=presses; i++) {
            
            unordered_set<int> t;
            
            for(int status : s) {
                
                t.insert(pressButton(status, 1, 1, n));
                t.insert(pressButton(status, 2, 2, n));
                t.insert(pressButton(status, 1, 2, n));
                t.insert(pressButton(status, 1, 3, n));
                
                
            }           
            
            s = t;
        }
        
        return s.size();        
        
    }
    
    
    int pressButton(int status, int start, int step, int n) {
        
        int flip = 0;
        
        for(int i=start-1; i<n; i+=step) {
            
            flip |= (1<<i);
        }
            
        return status ^ flip;
    }
    
    
};
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