<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)

        def dfs(ref, grid, i, j):
            if i < 0 or j < 0 or i >= n or j >= n or grid[i][j] == 0 or grid[i][j] == ref:
                return 0
            grid[i][j] = ref
            return 1 + dfs(ref, grid, i+1, j) + dfs(ref, grid, i-1, j) + dfs(ref, grid, i, j+1) + dfs(ref, grid, i, j-1)

        label = 2
        max_area = float('-inf')
        mp = {}

        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1:
                    cur = dfs(label, grid, i, j)
                    mp[label] = cur
                    label += 1
                    max_area = max(cur, max_area)

        for i in range(n):
            for j in range(n):
                if grid[i][j] == 0:
                    seen = set()
                    area = 0

                    if i>0:
                        seen.add(grid[i-1][j])
                    if j > 0:
                        seen.add(grid[i][j-1])
                    if i < n-1:
                        seen.add(grid[i+1][j])
                    if j < n-1:
                        seen.add(grid[i][j+1])
                    for k in seen:
                        area += mp.get(k, 0)
                    max_area = max(area+1, max_area)
        return max_area
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