<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 countSubIslands(self, grid1: List[List[int]], grid2: List[List[int]]) -> int:   
        m = len(grid1)
        n = len(grid1[0])
    
        visited2 = set()
        directions = [(1,0),(-1,0),(0,1),(0,-1)]
        islandDict = defaultdict(int)
        def dfs(i,j):
            for d in directions:
                ni = i + d[0]
                nj = j + d[1]

                if 0 <= ni < m and 0 <= nj < n and grid1[ni][nj] == 1 and (ni,nj) not in islandDict:
                    islandDict[(ni,nj)] = id1
                    dfs(ni,nj)
        id1 = 1
        for i in range(m):
            for j in range(n):
                if grid1[i][j] == 1 and (i,j) not in islandDict:
                    islandDict[(i,j)] = id1
                    dfs(i,j)
                    id1 += 1
       
        def countSub(i,j):
            nonlocal flag
         
            for d in directions:
                ni = i + d[0]
                nj = j + d[1]

                if 0 <= ni < m and 0 <= nj < n and grid2[ni][nj] == 1 and (ni,nj) not in visited2:

                    if (ni,nj) not in islandDict or islandDict[(ni,nj)] != id:
                        flag = False
                    visited2.add((ni,nj))
                    countSub(ni,nj)

        count = 0
        for i in range(m):
            for j in range(n):
            
                if grid2[i][j] == 1 and (i,j) in islandDict and (i,j) not in visited2:
                    flag = True
                    visited2.add((i,j))
                    id = islandDict[(i,j)]
                    countSub(i,j)

                    if flag:
                        count += 1
        return count


  


        

        
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