<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:        
        m = len(grid)
        n = len(grid[0])

        directions = [(1, 0), (0, 1), (0, -1), (-1, 0)]
        area = {}
        
        def dfs(i, j, size, group):
            if (grid[i][j] == 0) or (i, j) in seen:
                return size

            grid[i][j] = group
            size += 1
            seen.add((i, j))

            for di, dj in directions:
                if 0 <= i+di < m and 0 <= j+dj < n:
                    size = dfs(i+di, j+dj, size, group)

            return size

        seen = set()
        group = 2
        for i in range(m):
            for j in range(n):
                if grid[i][j] and (i, j) not in seen:
                    area[group] = dfs(i, j, 0, group)
                    group += 1

        if area:
            max_size = max(area.values())
        else:
            max_size = -1

        for i in range(m):
            for j in range(n):
                if grid[i][j] == 0:
                    new_area = 1
                    neighbour_group = set()
                    for di, dj in directions:
                        if 0 <= i+di < m and 0 <= j+dj < n and grid[i+di][j+dj]:
                            neighbour_group.add(grid[i+di][j+dj])

                    for ng in neighbour_group:
                        new_area += area[ng]
                    max_size = max(max_size, new_area)

        return max_size
70281