<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:
        
        islandMap = defaultdict(int)
        ROW = len(grid)
        COL = len(grid[0])

        visited = set()
        done = {}

        def dfs(i, j, islandId):

            if i < 0 or i >= ROW or j < 0 or j >= COL or (i, j) in visited or grid[i][j] != 1:
                return 0

            visited.add((i, j))

            res = 0
            res += dfs(i + 1, j, islandId)
            res += dfs(i - 1, j, islandId)
            res += dfs(i, j + 1, islandId)
            res += dfs(i, j - 1, islandId)

            done[i * ROW * COL + 20 + j] = islandId
            islandMap[islandId] = max(islandMap[islandId], 1 + res)
            return 1 + res

        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if (i, j) not in done.keys():
                    dfs(i, j, i * ROW * COL + 20 + j)

        if not islandMap.values():
            return 1
        res = max(islandMap.values())

        for i in range(len(grid)):
            for j in range(len(grid[0])):
                visited = set()
                maxIsland = 1
                if grid[i][j] == 0:
                    p = i + 1
                    q = j
                    key = p * ROW * COL + 20 + q
                    if key in done.keys() and done[key] not in visited:
                        maxIsland += islandMap[done[key]]
                        visited.add(done[key])
                    p = i - 1
                    q = j
                    key = p * ROW * COL + 20 + q
                    if key in done.keys() and done[key] not in visited:
                        maxIsland += islandMap[done[key]]
                        visited.add(done[key])
                    p = i
                    q = j + 1
                    key = p * ROW * COL + 20 + q
                    if key in done.keys() and done[key] not in visited:
                        maxIsland += islandMap[done[key]]
                        visited.add(done[key])
                    p = i
                    q = j - 1
                    key = p * ROW * COL + 20 + q
                    if key in done.keys() and done[p * ROW * COL + 20 + q] not in visited:
                        maxIsland += islandMap[done[p * ROW * COL + 20 + q]]
                        visited.add(done[p * ROW * COL + 20 + q])
                    res = max(res, maxIsland)

        return res
        


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