<p>You are given two <code>m x n</code> binary matrices <code>grid1</code> and <code>grid2</code> containing only <code>0</code>&#39;s (representing water) and <code>1</code>&#39;s (representing land). An <strong>island</strong> is a group of <code>1</code>&#39;s connected <strong>4-directionally</strong> (horizontal or vertical). Any cells outside of the grid are considered water cells.</p>

<p>An island in <code>grid2</code> is considered a <strong>sub-island </strong>if there is an island in <code>grid1</code> that contains <strong>all</strong> the cells that make up <strong>this</strong> island in <code>grid2</code>.</p>

<p>Return the <em><strong>number</strong> of islands in </em><code>grid2</code> <em>that are considered <strong>sub-islands</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/test1.png" style="width: 493px; height: 205px;" />
<pre>
<strong>Input:</strong> grid1 = [[1,1,1,0,0],[0,1,1,1,1],[0,0,0,0,0],[1,0,0,0,0],[1,1,0,1,1]], grid2 = [[1,1,1,0,0],[0,0,1,1,1],[0,1,0,0,0],[1,0,1,1,0],[0,1,0,1,0]]
<strong>Output:</strong> 3
<strong>Explanation: </strong>In the picture above, the grid on the left is grid1 and the grid on the right is grid2.
The 1s colored red in grid2 are those considered to be part of a sub-island. There are three sub-islands.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/03/testcasex2.png" style="width: 491px; height: 201px;" />
<pre>
<strong>Input:</strong> grid1 = [[1,0,1,0,1],[1,1,1,1,1],[0,0,0,0,0],[1,1,1,1,1],[1,0,1,0,1]], grid2 = [[0,0,0,0,0],[1,1,1,1,1],[0,1,0,1,0],[0,1,0,1,0],[1,0,0,0,1]]
<strong>Output:</strong> 2 
<strong>Explanation: </strong>In the picture above, the grid on the left is grid1 and the grid on the right is grid2.
The 1s colored red in grid2 are those considered to be part of a sub-island. There are two sub-islands.
</pre>

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

<ul>
	<li><code>m == grid1.length == grid2.length</code></li>
	<li><code>n == grid1[i].length == grid2[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>grid1[i][j]</code> and <code>grid2[i][j]</code> are either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution:

    def explore(self, grid2, grid1, row_idx, col_idx, visited_global):
        if visited_global[row_idx][col_idx] or grid2[row_idx][col_idx] == 0:
            return True
        visited_global[row_idx][col_idx] = True
        # go down
        # go right
        # go left
        
        res = res_down = res_right = res_left = res_up = True
        if grid1[row_idx][col_idx] == 0:
            res = False
        if row_idx < len(grid1) - 1:
            res_down = self.explore(grid2, grid1, row_idx=row_idx + 1, col_idx=col_idx, visited_global=visited_global)
        if row_idx > 0:
            res_up = self.explore(grid2, grid1, row_idx=row_idx - 1, col_idx=col_idx, visited_global=visited_global)
        if col_idx < len(grid1[0]) - 1:
            res_right = self.explore(grid2, grid1, row_idx=row_idx, col_idx=col_idx + 1, visited_global=visited_global)
        if col_idx > 0:
            res_left = self.explore(grid2, grid1, row_idx=row_idx, col_idx=col_idx - 1, visited_global=visited_global)
        return res and res_down and res_left and res_up and res_right

    def countSubIslands(self, grid1: List[List[int]], grid2: List[List[int]]) -> int:
        visited = [[False] * len(grid1[0]) for _ in range(len(grid1))]
        total = 0
        for row_idx, row in enumerate(grid2):
            for col_idx, element in enumerate(row):
                if visited[row_idx][col_idx] == True:
                    continue
                if element == 1:
                    # hit. need to explore
                    total += self.explore(grid2, grid1, row_idx, col_idx, visited_global=visited)
        return total
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