<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:
        ## strat: 
        # can only walk off if there is 1 on the border
        # for every 1 on the border: traverse 1s

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

        border = collections.deque()
        for i in range(n):
            if(grid[i][0] == 1):
                border.append((i, 0))
            if(grid[i][m-1] == 1):
                border.append((i, m-1))
        
        for i in range(m):
            if(grid[0][i] == 1):
                border.append((0,i))
            if(grid[n-1][i] == 1):
                border.append((n-1, i))


        directions = [(0,1), (-1,0), (1,0), (0,-1)]
        
        while border:
            x,y = border.pop()
            print(x,y)
            if(grid[x][y] == -1 or grid[x][y] == 0):
                continue
            
            grid[x][y] = -1

            for d_x, d_y in directions:
                new_x = x + d_x
                new_y = y + d_y
                if(new_x < 0 or new_x >= n or new_y < 0 or new_y >= m): continue
                border.append((new_x, new_y))
        
        count = 0
        for row in grid:
            for x in row:
                if x==1: count += 1
        return count

            

            
        
            
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