<p>You are given an <code>m x n</code> binary matrix <code>grid</code>, where <code>0</code> represents a sea cell and <code>1</code> represents a land cell.</p>

<p>A <strong>move</strong> consists of walking from one land cell to another adjacent (<strong>4-directionally</strong>) land cell or walking off the boundary of the <code>grid</code>.</p>

<p>Return <em>the number of land cells in</em> <code>grid</code> <em>for which we cannot walk off the boundary of the grid in any number of <strong>moves</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/enclaves1.jpg" style="width: 333px; height: 333px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,0,0],[1,0,1,0],[0,1,1,0],[0,0,0,0]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are three 1s that are enclosed by 0s, and one 1 that is not enclosed because its on the boundary.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/enclaves2.jpg" style="width: 333px; height: 333px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,0,1,0],[0,0,1,0],[0,0,0,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All 1s are either on the boundary or can reach the boundary.
</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;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

from typing import List

class Solution:
    def numEnclaves(self, grid: List[List[int]]) -> int:
        def dfs(i, j):
            # If out of bounds or water or already visited, stop the DFS.
            if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] == 0 or (i, j) in visited:
                return 0
            
            # Mark the cell as visited
            visited.add((i, j))
            
            # Initialize cell count as 1 (current cell)
            numCells = 1
            
            # Explore all four directions (up, right, down, left)
            directions = [(-1, 0), (0, 1), (1, 0), (0, -1)]
            for di, dj in directions:
                numCells += dfs(i + di, j + dj)
            
            return numCells
        
        visited = set()
        totalCount = 0
        
        # Mark all cells connected to the boundary as visited
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if (i == 0 or i == len(grid) - 1 or j == 0 or j == len(grid[0]) - 1) and grid[i][j] == 1:
                    dfs(i, j)
        
        # Count the number of cells in enclaves
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1 and (i, j) not in visited:
                    totalCount += dfs(i, j)
        
        return totalCount

56096