<p>You are given an <code>m x n</code> integer matrix <code>grid</code>, and three integers <code>row</code>, <code>col</code>, and <code>color</code>. Each value in the grid represents the color of the grid square at that location.</p>

<p>Two squares are called <strong>adjacent</strong> if they are next to each other in any of the 4 directions.</p>

<p>Two squares belong to the same <strong>connected component</strong> if they have the same color and they are adjacent.</p>

<p>The <strong>border of a connected component</strong> is all the squares in the connected component that are either adjacent to (at least) a square not in the component, or on the boundary of the grid (the first or last row or column).</p>

<p>You should color the <strong>border</strong> of the <strong>connected component</strong> that contains the square <code>grid[row][col]</code> with <code>color</code>.</p>

<p>Return <em>the final grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> grid = [[1,1],[1,2]], row = 0, col = 0, color = 3
<strong>Output:</strong> [[3,3],[3,2]]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> grid = [[1,2,2],[2,3,2]], row = 0, col = 1, color = 3
<strong>Output:</strong> [[1,3,3],[2,3,3]]
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> grid = [[1,1,1],[1,1,1],[1,1,1]], row = 1, col = 1, color = 2
<strong>Output:</strong> [[2,2,2],[2,1,2],[2,2,2]]
</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>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j], color &lt;= 1000</code></li>
	<li><code>0 &lt;= row &lt; m</code></li>
	<li><code>0 &lt;= col &lt; n</code></li>
</ul>

class Solution:
    DIRECTIONS = [
        (0, 1),
        (1, 0),
        (0, -1),
        (-1, 0)
    ]

    def is_valid_cell(self, grid: list[list[int]], row: int, col: int) -> bool:
        rows = len(grid)
        cols = len(grid[0])

        if row < 0 or col < 0 or row >= rows or col >= cols:
            return False

        return True

    def is_at_the_border(self, grid: list[list[int]], row: int, col: int, original_color: int, visited: set) -> bool:
        if (row, col) not in visited:
            return False

        rows = len(grid)
        cols = len(grid[0])

        if row == 0 or col == 0 or row == rows - 1 or col == cols - 1:
            return True

        for dr, dc in self.DIRECTIONS:
            nr = row + dr
            nc = col + dc
            if grid[nr][nc] != original_color and (nr, nc) not in visited:
                return True

        return False

    def colorBorder(self, grid: List[List[int]], row: int, col: int, color: int) -> List[List[int]]:
        queue = deque([(row, col)])
        visited = set()
        original_color = grid[row][col]

        while queue:
            r, c = queue.popleft()

            if not self.is_valid_cell(grid, r, c):
                continue

            if grid[r][c] != original_color:
                continue

            if (r, c) in visited:
                continue

            visited.add((r, c))

            if self.is_at_the_border(grid, r, c, original_color, visited):
                grid[r][c] = color

            for dr, dc in self.DIRECTIONS:
                queue.append((r + dr, c + dc))

        return grid

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