<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(r,c, index):
            seen = {(r,c)}
            stack = [(r,c)]
            while stack:
                r,c = stack.pop()
                grid[r][c] = index    
                for nr,nc in ((r-1,c),(r+1,c),(r,c+1),(r,c-1)):
                    if (nr,nc) not in seen and 0 <= nr < N and 0 <= nc < N and grid[nr][nc]:
                        stack.append((nr,nc))
                        seen.add((nr,nc))
            return len(seen)
        area = {}
        index = 2
        for x in range(len(grid)):
            for y in range(len(grid[0])):
                if grid[x][y] == 1:
                    area[index] = dfs(x,y,index)
                    index += 1
        result = max(area.values() or [0])
        for x in range(len(grid)):
            for y in range(len(grid[0])):
                if grid[x][y] == 0:
                    seen = set()
                    for nr, nc in ((x+1,y),(x-1,y),(x,y+1),(x,y-1)):
                        if 0 <= nr < N and 0 <= nc < N and grid[nr][nc] > 1:
                            seen.add(grid[nr][nc])
                    sum_adjacent = 0
                    for i in seen:
                        sum_adjacent += area[i]
                    result = max(result, 1 + sum_adjacent)
        return result

        '''
        ans = 0
        has_zero = False
        for x in range(len(grid)):
            for y in range(len(grid[0])):
                if grid[x][y] == 0:
                    has_zero = True
                    grid[x][y] = 1
                    ans = max(ans,dfs(x,y))
                    grid[x][y] = 0
        return ans if has_zero else N*N
        '''


            
        
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