<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 = len(grid)
        n = len(grid[0])


        def is_valid(row, col):
            if (0 <= row < m) and (0 <= col < n):
                if grid[row][col] == 1:
                    return True

        def is_boundary(row, col):
            if (row == 0) or (row == m-1):
                return True
            elif (col == 0) or (col == n-1):
                return True
            else:
                return False


        directions = [[0,1], [0,-1], [1,0], [-1,0]]

        def dfs(row, col, count):
            for dx, dy in directions:
                new_row, new_col = row + dx, col + dy
                if (new_row, new_col) not in seen and is_valid(new_row, new_col):                    
                    if is_boundary(new_row, new_col):
                        boundary[0] = True
                    seen.add((new_row, new_col))
                    count = dfs(new_row, new_col, count+1)
            return count

        seen = set()

        total = 0
        for row in range(m):
            for col in range(n):
                if grid[row][col] == 1:
                    if (row, col) not in seen and not is_boundary(row, col):
                        seen.add((row, col))
                        boundary = [False]
                        n_squares = dfs(row, col, count=1)
                        if not boundary[0]:
                            total += n_squares
        return total

        





        
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