<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:
    def flipLights(self, n: int, presses: int) -> int:
        global seen, buttons, computed
        seen = set()
        computed = dict()

        def dfs(n, presses):
            global seen, buttons, computed
            if presses == 0:
                seen.add(n)
                return
            if n in computed:
                if presses in computed[n]:
                    return
                computed[n].add(presses)
            else:
                computed[n] = {presses}
            for button in buttons:
                dfs(n ^ button, presses - 1)

        l = n
        buttons = [2 ** l - 1]
        
        b1 = ""
        b2 = ""
        for i in range(l):
            if i % 2 == 0:
                b1 += "1"
                b2 += "0"
            else:
                b2 += "1"
                b1 += "0"
            
        buttons += [int(b1, 2), int(b2, 2)]

        b3 = ["0"] * l
        for i in range(l):
            if 3 * i >= l:
                break
            b3[3 * i] = "1"
        buttons.append(int("".join(b3), 2))

        # print(2 ** l - 1, n, buttons)
        
        dfs(2 ** l - 1, presses)
        
        # print(seen)
        return len(seen)
17300