<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>

class Solution:
    def numEnclaves(self, grid: List[List[int]]) -> int:
        ROWS, COLS = len(grid), len(grid[0])
        visited = set()

        directions = [(-1, 0), (1, 0), (0, -1), (0, 1)]
        can_walk_off = set()

        def dfs(r,c):
            visited.add((r,c))
            can_walk_off.add((r,c))

            for dr,dc in directions:
                nr,nc = r + dr,c + dc
                if (0 <= nr < ROWS and
                    0 <= nc < COLS and
                    grid[nr][nc] == 1 and
                    (nr,nc) not in visited):
                    can_walk_off.add((nr,nc))
                    dfs(nr,nc)
        
        for r in range(ROWS):
            for c in [0,COLS-1]:
                if grid[r][c] == 1:
                    
                    dfs(r,c)

        for c in range(COLS):
            for r in [0,ROWS-1]:
                if grid[r][c] == 1:
                    dfs(r,c)
        
        count = 0
        for r in range(ROWS):
            for c in range(COLS):
                if grid[r][c] == 1:
                    count += 1

        return count - len(can_walk_off)

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