<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>

import copy
from typing import List

class Solution:
    def countSubIslands(self, grid1: List[List[int]], grid2: List[List[int]]) -> int:
        rows = len(grid1)
        cols = len(grid1[0])
        
        def dfs(r, c, grid):
            if not (0 <= r < rows and 0 <= c < cols) or grid[r][c] == 0:
                return
            grid[r][c] = 0
            for dr, dc in [(1, 0), (-1, 0), (0, 1), (0, -1)]:
                dfs(r + dr, c + dc, grid)
        
        def dfs2(r, c, grid, values):
            if not (0 <= r < rows and 0 <= c < cols) or grid[r][c] == 0:
                return
            grid[r][c] = 0
            values.append((r, c))
            for dr, dc in [(1, 0), (-1, 0), (0, 1), (0, -1)]:
                dfs2(r + dr, c + dc, grid, values)
            return values
        
        # Step 1: Find and count the number of islands in grid1
        correct_grid1 = copy.deepcopy(grid1)
        no_of_islands = 0
        for r in range(rows):
            for c in range(cols):
                if grid1[r][c] == 1:
                    dfs(r, c, grid1)
                    no_of_islands += 1

        # Step 2: Find sub-islands in grid2 that are also islands in correct_grid1
        no_of_sub_islands = 0
        for r2 in range(rows):
            for c2 in range(cols):
                if grid2[r2][c2] == 1:
                    values = dfs2(r2, c2, grid2, [])
                    
                    # Check if the sub-island in grid2 is part of an island in grid1
                    is_sub_island = all(correct_grid1[r][c] == 1 for r, c in values)
                    
                    if is_sub_island:
                        no_of_sub_islands += 1
        return no_of_sub_islands

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