<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 check(self, i, j, n, m):
        return 0 <= i < n and 0 <= j < m

    def numEnclaves_help(self, x, y, grid, visited, n, m):
        visited[(x, y)] = True
        count = 1
        dx = [1, 0, -1, 0]
        dy = [0, 1, 0, -1]
        for k in range(4):
            new_x = x + dx[k]
            new_y = y + dy[k]
            if self.check(new_x, new_y, n, m) and (new_x, new_y) not in visited and grid[new_x][new_y] == 1:
                count += self.numEnclaves_help(new_x, new_y, grid, visited, n, m)
        return count

    def numEnclaves(self, grid: List[List[int]]) -> int:
        visited = {}
        n = len(grid)
        m = len(grid[0])
        total_land_cells = 0
        
        # Count all land cells
        for i in range(n):
            for j in range(m):
                if grid[i][j] == 1:
                    total_land_cells += 1
        
        # Perform DFS/BFS from the boundary to mark all reachable land cells
        for i in range(n):
            for j in [0, m-1]:
                if grid[i][j] == 1 and (i, j) not in visited:
                    self.numEnclaves_help(i, j, grid, visited, n, m)
        
        for j in range(m):
            for i in [0, n-1]:
                if grid[i][j] == 1 and (i, j) not in visited:
                    self.numEnclaves_help(i, j, grid, visited, n, m)
        
        # Count all land cells that are not reachable from the boundary
        count_enclaves = 0
        for i in range(1, n-1):
            for j in range(1, m-1):
                if grid[i][j] == 1 and (i, j) not in visited:
                    count_enclaves += self.numEnclaves_help(i, j, grid, visited, n, m)
        
        return count_enclaves
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