<p>Given an integer <code>n</code>, return <em>a binary string representing its representation in base</em> <code>-2</code>.</p>

<p><strong>Note</strong> that the returned string should not have leading zeros unless the string is <code>&quot;0&quot;</code>.</p>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> &quot;110&quot;
<strong>Explantion:</strong> (-2)<sup>2</sup> + (-2)<sup>1</sup> = 2
</pre>

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

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> &quot;111&quot;
<strong>Explantion:</strong> (-2)<sup>2</sup> + (-2)<sup>1</sup> + (-2)<sup>0</sup> = 3
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> &quot;100&quot;
<strong>Explantion:</strong> (-2)<sup>2</sup> = 4
</pre>

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

<ul>
	<li><code>0 &lt;= n &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def baseNeg2(self, n: int) -> str:
        if not n:
            return str(n)
        masks = {0: "10", 1: "11", 2: "00", 3: "01"}
        upperBound = [0, 1]
        while upperBound[-1] < n:
            upperBound.append((upperBound[-1] - upperBound[-2]) * 4 + upperBound[-1])
        upperBound.pop()
        result = "1"
        gap, length = n - upperBound[-1] - 1, len(upperBound) - 1
        for _ in range(length):
            x, gap = divmod(gap, upperBound.pop() - upperBound[-1])
            result += masks[x]
        return result
16500