<p>Given a 2D&nbsp;<code>grid</code> consists of <code>0s</code> (land)&nbsp;and <code>1s</code> (water).&nbsp; An <em>island</em> is a maximal 4-directionally connected group of <code><font face="monospace">0</font>s</code> and a <em>closed island</em>&nbsp;is an island <strong>totally</strong>&nbsp;(all left, top, right, bottom) surrounded by <code>1s.</code></p>

<p>Return the number of <em>closed islands</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/31/sample_3_1610.png" style="width: 240px; height: 120px;" /></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1,1,0],[1,0,0,0,0,1,1,0],[1,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,1],[1,1,1,1,1,1,1,0]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
Islands in gray are closed because they are completely surrounded by water (group of 1s).</pre>

<p><strong class="example">Example 2:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/31/sample_4_1610.png" style="width: 160px; height: 80px;" /></p>

<pre>
<strong>Input:</strong> grid = [[0,0,1,0,0],[0,1,0,1,0],[0,1,1,1,0]]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1,1],
&nbsp;              [1,0,0,0,0,0,1],
&nbsp;              [1,0,1,1,1,0,1],
&nbsp;              [1,0,1,0,1,0,1],
&nbsp;              [1,0,1,1,1,0,1],
&nbsp;              [1,0,0,0,0,0,1],
               [1,1,1,1,1,1,1]]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= grid.length, grid[0].length &lt;= 100</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;=1</code></li>
</ul>

class Solution:
    def closedIsland(self, grid: List[List[int]]) -> int:
        directions = [(0,1),(1,0),(0,-1),(-1,0)]
        n = len(grid)
        m = len(grid[0])

        def inbound(row, col):
            return ((0 <= row < n) and (0 <= col < m) and (grid[row][col] == 0))


        def dfs(row, col):
            grid[row][col] = 1
            for x, y in directions:
                new_row = row + x
                new_col = col + y

                if inbound(new_row,new_col):
                    dfs(new_row,new_col)
        
        for i in range(m):
            if grid[0][i] == 0:
                dfs(0,i)
        for j in range(n):
            if grid[j][0] == 0:
                dfs(j,0)
        for k in range(m):
            if grid[n-1][k] == 0:
                dfs(n - 1,k)
        for l in range(n):
            if grid[l][m-1] == 0:
                dfs(l,len(grid[0]) - 1)
        
        count = 0
        for a in range(len(grid)):
            for b in range(len(grid[0])):
                if grid[a][b] == 0:
                    count += 1
                    dfs(a,b)
        return count
17300