<p>You are given an <code>n x n</code> binary matrix <code>grid</code>. You are allowed to change <strong>at most one</strong> <code>0</code> to be <code>1</code>.</p>

<p>Return <em>the size of the largest <strong>island</strong> in</em> <code>grid</code> <em>after applying this operation</em>.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>s.</p>

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

<pre>
<strong>Input:</strong> grid = [[1,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,0]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Change the 0 to 1 and make the island bigger, only one island with area = 4.</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Can&#39;t change any 0 to 1, only one island with area = 4.
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= 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 largestIsland(self, grid: List[List[int]]) -> int:
        island_id = -1
        idToSize = collections.defaultdict(int)
        ROWS, COLS = len(grid), len(grid[0])
       

        seen = set()
        def island_size(i,j):
            if i < 0 or j < 0 or i >= ROWS or j >=COLS or grid[i][j] == 0 or (i,j) in seen:
                return 0

            seen.add((i,j))
            grid[i][j] = island_id
            
            return 1 + (island_size(i+1,j)+
                        island_size(i-1, j)+
                        island_size(i, j-1)+
                        island_size(i, j+1))
         
        for i in range(ROWS):
            for j in range(COLS):
                if grid[i][j] == 1:
                    size = island_size(i,j)
                    idToSize[island_id] = size
                    island_id -=1

        max_area = 0

        directions = ((1,0), (-1, 0), (0,1), (0,-1))

        for i in range(ROWS):
            for j in range(COLS):
                if grid[i][j] == 0:
                    #flip a 0 to 1 annd find the surrondings
                    area = 1

                    surrounding_islands_id = set()
                    for d1, d2 in directions:
                        new_i = i + d1
                        new_j = j + d2

                        if 0 <= new_i < ROWS and 0 <= new_j < COLS and grid[new_i][new_j] != 0:
                            surrounding_islands_id.add(grid[new_i][new_j])
                        
                    for id in surrounding_islands_id:
                        area+= idToSize[id]
                
                    max_area = max(max_area, area)


        return max_area if max_area != 0 else ROWS * COLS

                

      
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