<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 getN(x,y):
            for i,j in [[x-1,y],[x+1,y],[x,y-1],[x,y+1]]:
                if 0<=i<N and 0<=j<N:
                    yield i,j
        def getArea(x,y,index):
            grid[x][y] = index
            area = 1
            for nx, ny in getN(x,y):
                if grid[nx][ny]==1:
                    area+=getArea(nx,ny,index)
            return area

        area = {}
        index = 2
        for i in range(N):
            for j in range(N):
                if grid[i][j] == 1:
                    area[index] = getArea(i,j,index)
                    index+=1
        max_area = 1
        for i in range(N):
            for j in range(N):
                if grid[i][j] == 0:
                    seen = {grid[nx][ny] for nx,ny in getN(i,j) if grid[nx][ny]>0}
                    max_area = max(max_area, 1+sum(area[i] for i in seen))
        max_area = max(max_area, max(area.values() or [0]))
        return max_area

26818