<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:
    def colorBorder(self, grid: List[List[int]], row: int, col: int, color: int) -> List[List[int]]:
        m = len(grid)
        n = len(grid[0])
        region_color = grid[row][col]

        stack = [(row, col)]
        visited = set()

        border = set()
        while len(stack) > 0:
            r, c = stack.pop()

            if (r, c) in visited:
                continue
            visited.add((r, c))

            if r > 0 and grid[r - 1][c] == region_color:
                stack.append((r - 1, c))
            else:
                border.add((r, c))
            if r < m - 1 and grid[r + 1][c] == region_color:
                stack.append((r + 1, c))
            else:
                border.add((r, c))
            if c > 0 and grid[r][c - 1] == region_color:
                stack.append((r, c - 1))
            else:
                border.add((r, c))
            if c < n - 1 and grid[r][c + 1] == region_color:
                stack.append((r, c + 1))
            else:
                border.add((r, c))
        
        for r, c in border:
            grid[r][c] = color

        return grid
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