<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:
        rows = len(grid)
        if not rows:
            return 0
        cols = len(grid[0])
        if not cols:
            return 0
        ans = 0
        id = 0
        for i in range(rows):
            for j in range(cols):
                if grid[i][j] == 1:
                    sz = self.visit(i, j, grid, id)
                    if sz == rows * cols:
                        return sz
                    ans = max(sz, ans)
                    id += 1

        dirs = [[0,1], [1,0], [0,-1], [-1,0]]
        for i in range(rows):
            for j in range(cols):
                if grid[i][j] == 0:
                    islands = {}
                    sz = 1
                    for d in dirs:
                        row = i + d[0]
                        col = j + d[1]
                        if row >= 0 and row < rows and col >= 0 and col < cols and grid[row][col] != 0:
                          islands[grid[row][col][0]] = grid[row][col][1]  
                    for k in islands:
                        sz += islands[k]
                    ans = max(ans, sz)
        return ans
    
    def visit(self, i, j, grid, id):
        if grid[i][j] == 0:
            return 0
        rows = len(grid)
        cols = len(grid[0])
        visited = set([(i,j)])
        dirs = [[0,1], [1,0], [0,-1], [-1,0]]
        q = [[i,j]]
        while q:
            x, y = q.pop(0)
            for d in dirs:
                row = x + d[0]
                col = y + d[1]
                if row >= 0 and row < rows and col >= 0 and col < cols and (row,col) not in visited and grid[row][col] != 0:
                    visited.add((row,col))
                    q.append([row,col])
        sz = len(visited)
        for point in visited:
            x = point[0]
            y = point[1]
            grid[x][y] = (id, sz)
        return sz
            

        
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