<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:

        COL_SIZE = len(grid)
        ROW_SIZE = len(grid[0])

        islands = {}
        islands_total = {}

        def visitLand(x,y):
            nonlocal grid
            nonlocal islands
            nonlocal islands_total

            visited = set()
            queue = [(x,y)]

            while queue:
                row,col = queue.pop()
                visited.add((row,col))
                
                nextToVisit = [
                    (row+1,col),
                    (row-1,col),
                    (row,col+1),
                    (row,col-1),
                ]
                for r,c in nextToVisit:
                    if 0 <= r < COL_SIZE and 0 <= c < ROW_SIZE and (r,c) not in visited and grid[r][c] ==1:
                        queue.append((r,c))
            
            total = len(visited)
            for row,col in visited:
                islands[(row,col)] = (x,y)
            islands_total[(x,y)] = total
        
        def getIslandLand(x,y):
            nonlocal grid
            nonlocal islands
            nonlocal islands_total

            queue = [
                (x+1,y),
                (x-1,y),
                (x,y+1),
                (x,y-1),
            ]

            distinctIslands = set()
            for r,c in queue:
                if 0 <= r < COL_SIZE and 0 <= c < ROW_SIZE and (r,c) and grid[r][c] == 1:
                    distinctIslands.add(islands[(r,c)])
            
            landOfNewIsland = 1
            for x,y in distinctIslands:
                landOfNewIsland += islands_total[(x,y)]
            
            return landOfNewIsland


        for x in range(0,len(grid)):
            for y in range(0,len(grid[x])):
                if grid[x][y] == 1 and (x,y) not in islands.keys():
                    visitLand(x,y)
        
        if islands_total:
            largestIsland = max(islands_total.values())
        else:
            largestIsland = 1
        for x in range(0,len(grid)):
            for y in range(0,len(grid[x])):
                if grid[x][y] == 0:
                    largestIsland = max(largestIsland,getIslandLand(x,y))
        
        return largestIsland
    

        
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