<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:
        def dfs(i, j, color):
            s = 1
            grid[i][j] = color
            for ai, aj in adj(i, j):
                if grid[ai][aj] == 1:
                    s += dfs(ai, aj, color)
            return s

        size = {0: 0}
        COLOR = 2
        n = len(grid)
        zeros = []
        adj = lambda i, j: ((ai, aj) for ai, aj in [(i + 1, j), (i - 1, j), (i, j + 1), (i, j - 1)] if 0 <= ai < n and 0 <= aj < n)

        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1:
                    size[COLOR] = dfs(i, j, COLOR)
                    COLOR += 1
                elif grid[i][j] == 0:
                    zeros.append((i, j))

        return max(list(size.values()) + [1 + sum(size[c] for c in set(grid[ai][aj] for ai, aj in adj(i, j))) for i, j in zeros])
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