<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:
        groups = defaultdict(int)
        group_cnt = defaultdict(int)
        
        group = 1
        m, n = len(grid), len(grid[0])
        for r in range(m):
            for c in range(n):
                if grid[r][c] == 1 and (r, c) not in groups:
                    groups[(r, c)] = group
                    group_cnt[group] += 1
                    dq = deque([(r, c)])
                    while dq:
                        x, y = dq.popleft()
                        for nx, ny in (x-1, y), (x+1, y), (x, y-1), (x, y+1):
                            if 0 <= nx < m and 0 <= ny < n and grid[nx][ny] == 1 and (nx, ny) not in groups:
                                groups[(nx, ny)] = group
                                group_cnt[group] += 1
                                dq.append((nx, ny))
                    group += 1
        
        if len(groups) == 0:
            return 1
        elif len(groups) == m * n:
            return m * n

        ans = 0
        for r in range(m):
            for c in range(n):
                if grid[r][c] == 0:
                    lst = set()
                    for x, y in (r-1, c), (r+1, c), (r, c-1), (r, c+1):
                        if 0 <= x < m and 0 <= y < n and (x, y) in groups:
                            lst.add(groups[(x, y)])

                    cur_max = sum(group_cnt[i] for i in lst) + 1
                    ans = max(ans, cur_max)
        
        return ans
42493