<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]]:
        ROWS, COLS = len(grid), len(grid[0])

        def helper(r, c, k):
            level = min(r, c, ROWS - r - 1, COLS - c - 1)
            # print(level)

            perim = 2*COLS + 2*ROWS - 8*level - 4
            # print(perim)
            if r == level and c != level:
                k += c - level
            elif c == COLS - level - 1 and r != level:
                k += COLS - 2*level - 1 + r - level
            elif r == ROWS - level - 1 and c != COLS - level - 1:
                k += COLS - 2*level - 1 + ROWS - 2*level - 1 + COLS - level - 1 - c
            else:
                k += 2*COLS - 4*level - 2 + ROWS - 2*level - 1 + ROWS - 1 - level - r

            p = k % perim
            # print(p)

            new_r = level
            new_c = level

            move_right = min(p, COLS - 2*level - 1)
            new_c += move_right
            p -= move_right

            move_down = min(p, ROWS - 2*level - 1)
            new_r += move_down
            p -= move_down

            move_left = min(p, COLS - 2*level - 1)
            new_c -= move_left
            p -= move_left

            move_up = min(p, ROWS - 2*level - 1)
            new_r -= move_up
            p -= move_up

            return grid[new_r][new_c]
        
        new_grid = [[0] * COLS for _ in range(ROWS)]
        for i in range(ROWS):
            for j in range(COLS):
                new_grid[i][j] = helper(i,j,k)
        return new_grid

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