<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:
        n = len(grid)
        clusters = {}
        vis = [[False] * n for _ in range(n)]
        clusterSize = []
        def dfs(i, j, cl):
            vis[i][j] = True
            clusters[(i, j)] = cl
            clusterSize[cl] += 1
            for x, y in [(i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1)]:
                if x < 0 or y < 0 or x >= n or y >= n: continue
                if grid[x][y] == 1 and not vis[x][y]:
                    dfs(x, y, cl)
        
        cl = 0
        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1 and not vis[i][j]:
                    clusterSize.append(0)
                    dfs(i, j, cl)
                    cl += 1
        
        if cl == 0: return 1
        res = max(clusterSize)
        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1: continue

                surr = set()
                for x, y in [(i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1)]:
                    if x < 0 or y < 0 or x >= n or y >= n: continue
                    if grid[x][y] == 1:
                        surr.add(clusters[(x, y)])
                
                tot = 1
                for c in surr:
                    tot += clusterSize[c]
                
                res = max(res, tot)

        return res
53893