<p>An <strong>n-bit gray code sequence</strong> is a sequence of <code>2<sup>n</sup></code> integers where:</p>

<ul>
	<li>Every integer is in the <strong>inclusive</strong> range <code>[0, 2<sup>n</sup> - 1]</code>,</li>
	<li>The first integer is <code>0</code>,</li>
	<li>An integer appears <strong>no more than once</strong> in the sequence,</li>
	<li>The binary representation of every pair of <strong>adjacent</strong> integers differs by <strong>exactly one bit</strong>, and</li>
	<li>The binary representation of the <strong>first</strong> and <strong>last</strong> integers differs by <strong>exactly one bit</strong>.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>any valid <strong>n-bit gray code sequence</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> [0,1,3,2]
<strong>Explanation:</strong>
The binary representation of [0,1,3,2] is [00,01,11,10].
- 0<u>0</u> and 0<u>1</u> differ by one bit
- <u>0</u>1 and <u>1</u>1 differ by one bit
- 1<u>1</u> and 1<u>0</u> differ by one bit
- <u>1</u>0 and <u>0</u>0 differ by one bit
[0,2,3,1] is also a valid gray code sequence, whose binary representation is [00,10,11,01].
- <u>0</u>0 and <u>1</u>0 differ by one bit
- 1<u>0</u> and 1<u>1</u> differ by one bit
- <u>1</u>1 and <u>0</u>1 differ by one bit
- 0<u>1</u> and 0<u>0</u> differ by one bit
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [0,1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 16</code></li>
</ul>

class Solution:
    def grayCode(self, n: int) -> List[int]:
        
        r = []
        array = [ False for _ in range(n) ]  
        i = 2**n # number of iterations
        offset = i//2 

        for x in range(i):
            # val = val if (x+1)%2 else not val
            # val = val if (x+2)%4 else not val
            # val = val if (x+4)%8 else not val 

            val = i
            for j in range(n):
                array[j] = array[j] if (x+val//2)%val else not array[j]
                val//=2

            r.append(array[:])
        
        return [ int('0b' + ''.join([ str(int(x)) for x in item ]),2) for item in r ]

        # iter = 1 * 2
        # 0 
        # 1

        # iter = 1 * 2 * 2
        # 0 0
        # 0 1
        # 1 1
        # 1 0
        
        # iter =  1 * 2 * 2 * 2
        # 0 0 0 x = 1 
        # 0 0 1 x = 2
        # 0 1 1 x = 3
        # 0 1 0
        # 1 1 0
        # 1 1 1
        # 1 0 1
        # 1 0 0
31900