<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: List[List[int]], k: int) -> List[List[int]]:
        m, n = len(grid), len(grid[0])
        
        # Function to extract a layer as a list
        def extract_layer(layer):
            elements = []
            # Top row (left to right)
            for col in range(layer, n - layer):
                elements.append(grid[layer][col])
            # Right column (top to bottom)
            for row in range(layer + 1, m - layer):
                elements.append(grid[row][n - layer - 1])
            # Bottom row (right to left)
            for col in range(n - layer - 2, layer - 1, -1):
                elements.append(grid[m - layer - 1][col])
            # Left column (bottom to top)
            for row in range(m - layer - 2, layer, -1):
                elements.append(grid[row][layer])
            
            return elements
        
        # Function to place the rotated elements back into the layer
        def place_layer(layer, rotated):
            idx = 0
            # Top row (left to right)
            for col in range(layer, n - layer):
                grid[layer][col] = rotated[idx]
                idx += 1
            # Right column (top to bottom)
            for row in range(layer + 1, m - layer):
                grid[row][n - layer - 1] = rotated[idx]
                idx += 1
            # Bottom row (right to left)
            for col in range(n - layer - 2, layer - 1, -1):
                grid[m - layer - 1][col] = rotated[idx]
                idx += 1
            # Left column (bottom to top)
            for row in range(m - layer - 2, layer, -1):
                grid[row][layer] = rotated[idx]
                idx += 1

        # Process each layer
        for layer in range(min(m, n) // 2):
            # Extract the current layer
            elements = extract_layer(layer)
            # Determine the number of rotations, as k can be large
            total_elements = len(elements)
            rotation_steps = k % total_elements
            # Rotate the layer's elements
            rotated = elements[rotation_steps:] + elements[:rotation_steps]
            # Place the rotated elements back into the grid
            place_layer(layer, rotated)
        
        return grid
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