<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:
        m, n = len(grid), len(grid[0])
        
        def is_valid(i, j):
            return i in range(m) and j in range(n)
        
        dirs = [(-1, 0), (1, 0), (0, -1), (0, 1)]
        
        def get_neighbors(i, j):
            for di, dj in dirs:
                ni, nj = i + di, j + dj
                if is_valid(ni, nj): yield (ni, nj)
                    
        seen = set()
        
        def mark_enclave(i, j):
            ans = 1
            
            seen.add((i, j))
            
            for ni, nj in get_neighbors(i, j):
                if (ni, nj) in seen or grid[ni][nj] == 0: continue
                ans += mark_enclave(ni, nj)
                
            return ans
        
        ans = 0
        
        def should_explore(i, j):
            return (i, j) not in seen and grid[i][j] == 1

        def explore_range(nodes):
            for i, j in nodes:

                if (i, j) in seen or grid[i][j] == 0: continue
                mark_enclave(i, j)

        explore_range((i, 0) for i in range(m))
        explore_range((i, n - 1) for i in range(m))
        explore_range((0, j) for j in range(n))
        explore_range((m - 1, j) for j in range(n))
        
        for i in range(1, m - 1):
            for j in range(1, n - 1):
                if grid[i][j] == 1 and (i, j) not in seen:
                    ans += 1
                    
        return ans

# [0,0,0,1,1,1,0,1,0,0],
# [1,1,0,0,0,1,0,1,1,1],
# [0,0,0,1,1,1,0,1,0,0],
# [0,1,1,0,0,0,1,0,1,0],
# [0,1,1,1,1,1,0,0,1,0],
# [0,0,1,0,1,1,1,1,0,1],
# [0,1,1,0,0,0,1,1,1,1],
# [0,0,1,0,0,1,0,1,0,1],
# [1,0,1,0,1,1,0,0,0,0],
# [0,0,0,0,1,1,0,0,0,1]
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