<p>Given a positive integer <code>n</code>, generate an <code>n x n</code> <code>matrix</code> filled with elements from <code>1</code> to <code>n<sup>2</sup></code> in spiral order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/spiraln.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> [[1,2,3],[8,9,4],[7,6,5]]
</pre>

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

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

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

<ul>
	<li><code>1 &lt;= n &lt;= 20</code></li>
</ul>

class Solution:
    def generateMatrix(self, n: int) -> List[List[int]]:
        out = [[0] * n for i in range(n)]
        x, y, dx, dy = 0, 0, 1, 0

        for counter in range(1, n ** 2 + 1):
            out[y][x] = counter

            # dx = 1, dy = 0
            # dx = 0, dy = 1
            # dx = -1, dy = 0
            # dx = 0, dy = -0
            # repeat...
            if not 0 <= x+dx < n or not 0 <= y+dy < n or out[y+dy][x+dx] != 0:
                dx, dy = -dy, dx

            x += dx
            y += dy

        return out
16000