<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:
        n = (1 << n) - 1

        even_mask = 1
        for i in range(1000):
            even_mask *= 4
            even_mask += 2
        
        odd_mask = ~even_mask

        b4_mask = 1
        for i in range(1000):
            b4_mask *= 8
            b4_mask += 1

        even_mask &= n
        odd_mask &= n
        b4_mask &= n

        unique_possibilities = set()
        visited = set() # tuples of the form ( bitstring, level )

        stack = [(n, 0)]

        while len(stack) > 0:
            node = stack.pop()
            bit, num_presses = node

            visited.add(node)
            
            if num_presses == presses:
                unique_possibilities.add(bit)
                continue

            for func in [self.button_1, self.button_2, self.button_3, self.button_4]:
                new_node = (func(bit, n, even_mask, odd_mask, b4_mask), num_presses + 1)
                
                if new_node not in visited:
                    stack.append(new_node)
            

        return len(unique_possibilities)


    def button_1(self, bit, n, even_mask, odd_mask, b4_mask):
        """
        flip everything by just not-ting it
        """
        return ~bit & n
    

    def button_2(self, bit, n, even_mask, odd_mask, b4_mask):
        """
        flip all the bits at even positions
        """
        # even_digits = bit & even_mask
        flipped_even_bits = (~bit) & even_mask
        return (bit & odd_mask) + flipped_even_bits

    
    def button_3(self, bit, n, even_mask, odd_mask, b4_mask):
        """
        flip all the bits at odd positions
        """
        flipped_odd_bits = (~bit) & odd_mask

        return (bit & even_mask) + flipped_odd_bits

    
    def button_4(self, bit, n, even_mask, odd_mask, b4_mask):
        """
        flip all the bits at indices 3k + 1, where k == 0, 1, 2, etc.
        """
        b4_bits = ~bit
        flipped_b4_bits = b4_bits & b4_mask

        # b4_bits = bit & b4_mask
        # flipped_b4_bits = ~b4_bits
        # flipped_b4_bits &= n

        return (bit & (~b4_mask & n)) + flipped_b4_bits    

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