<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:

        islandIdMapping = {}
        islandCount = {-1:0}
        islandId = 0
        def getCountIsland(x,y):
            nonlocal islandIdMapping,islandCount,islandId,grid

            queue = [[x,y]]

            visited = set()
            
            while queue:
                x,y = queue.pop()
                visited.add((x,y))

                for row,col in [(x+1,y),(x-1,y),(x,y+1),(x,y-1)]:

                    if 0<=row<len(grid) and 0<=col<len(grid[row]) and grid[row][col] == 1 and (row,col) not in visited:
                        queue.append([row,col])
            
            for _x,_y in visited:
                islandIdMapping[(_x,_y)] = islandId
            islandCount[islandId] = len(visited)
            islandId +=1

        for x in range(len(grid)):
            for y in range(len(grid[x])):
                if (x,y) not in islandIdMapping and grid[x][y] == 1:
                    getCountIsland(x,y)
        
        def getMaxSize(x,y):
            nonlocal islandIdMapping,islandCount,islandId,grid

            possibleIslands = set()
            for row,col in [(x+1,y),(x-1,y),(x,y+1),(x,y-1)]:
                if 0<=row<len(grid) and 0<=col<len(grid[row]) and grid[row][col] == 1:
                    possibleIslands.add(islandIdMapping[(row,col)])
            print(possibleIslands)
            possibleArea = 1
            for i_id in possibleIslands:
                possibleArea += islandCount[i_id]
            return possibleArea
            

        largestIsland = max(islandCount.values())
        for x in range(len(grid)):
            for y in range(len(grid[x])):
                if grid[x][y] == 0:
                    largestIsland = max(largestIsland,getMaxSize(x,y))
        
        return largestIsland


        
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