<p>You are given an <code>m x n</code> integer matrix <code>grid</code>​​​, where <code>m</code> and <code>n</code> are both <strong>even</strong> integers, and an integer <code>k</code>.</p>

<p>The matrix is composed of several layers, which is shown in the below image, where each color is its own layer:</p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid.png" style="width: 231px; height: 258px;" /></p>

<p>A cyclic rotation of the matrix is done by cyclically rotating <strong>each layer</strong> in the matrix. To cyclically rotate a layer once, each element in the layer will take the place of the adjacent element in the <strong>counter-clockwise</strong> direction. An example rotation is shown below:</p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/22/explanation_grid.jpg" style="width: 500px; height: 268px;" />
<p>Return <em>the matrix after applying </em><code>k</code> <em>cyclic rotations to it</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/19/rod2.png" style="width: 421px; height: 191px;" />
<pre>
<strong>Input:</strong> grid = [[40,10],[30,20]], k = 1
<strong>Output:</strong> [[10,20],[40,30]]
<strong>Explanation:</strong> The figures above represent the grid at every state.
</pre>

<p><strong class="example">Example 2:</strong></p>
<strong><img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid5.png" style="width: 231px; height: 262px;" /></strong> <strong><img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid6.png" style="width: 231px; height: 262px;" /></strong> <strong><img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/ringofgrid7.png" style="width: 231px; height: 262px;" /></strong>

<pre>
<strong>Input:</strong> grid = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], k = 2
<strong>Output:</strong> [[3,4,8,12],[2,11,10,16],[1,7,6,15],[5,9,13,14]]
<strong>Explanation:</strong> The figures above represent the grid at every state.
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>2 &lt;= m, n &lt;= 50</code></li>
	<li>Both <code>m</code> and <code>n</code> are <strong>even</strong> integers.</li>
	<li><code>1 &lt;= grid[i][j] &lt;=<sup> </sup>5000</code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
</ul>
class Solution:
    def rotateGrid(self, grid, k):
        def rotateLayer(layer):
            top, left = layer, layer
            bottom, right = len(grid) - 1 - layer, len(grid[0]) - 1 - layer
            layer_size = (bottom - top + 1) * 2 + (right - left + 1) * 2 - 4
            rotations = k % layer_size
            
            for _ in range(rotations):
                temp = grid[top][left]
                for i in range(left, right):
                    grid[top][i] = grid[top][i + 1]
                for i in range(top, bottom):
                    grid[i][right] = grid[i + 1][right]
                for i in range(right, left, -1):
                    grid[bottom][i] = grid[bottom][i - 1]
                for i in range(bottom, top, -1):
                    grid[i][left] = grid[i - 1][left]
                grid[top + 1][left] = temp

        layers = min(len(grid) // 2, len(grid[0]) // 2)
        for layer in range(layers):
            rotateLayer(layer)
        
        return grid
212