<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 traverse(self, state, rem, seen):
        if rem == 0:
            self.resp.add(state)
            return
        rem -= 1
        for optn in self.options:
            newstate = state ^ optn
            if ((newstate, rem) in seen):
                continue
            seen.add((newstate, rem))
            self.traverse(newstate, rem, seen)

    def flipLights(self, n: int, presses: int) -> int:
        #even pos - bitwise xor
        #switch all - not
        #
        mask_evn = ["0"]*n
        mask_odd = ["0"]*n
        mask_alt = ["0"]*n
        mask_not = ["1"]*n
        k = 0
        for index in range(n):
            if index % 2 == 0:
                mask_evn[index] = "1"
            if index % 2 == 1:
                mask_odd[index] = "1"
            if index % ((3*k) + 1) == 0:
                mask_alt[index] = "1"
                k += 1

        mask_evn.reverse()
        mask_odd.reverse()
        mask_alt.reverse()
        mask_evn = "".join(mask_evn)
        mask_odd = "".join(mask_odd)
        mask_alt = "".join(mask_alt)
        mask_not = "".join(mask_not)

        self.options = [int(mask_alt, 2), int(mask_odd, 2), int(mask_evn, 2), int(mask_not, 2)]
        self.resp = set()
        state = int("1"*n, 2)
        seen = set()
        self.traverse(state, presses, seen)
        return len(self.resp)


            
19000