<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:
        
        visited = set()
        g = [[0]*len(grid[0]) for i in range(len(grid))]

        def isCellPosValid(i,j):
            a = i >= 0 and i < len(grid)
            b = j >= 0 and j < len(grid[0])
            if not a or not b:
                return False
            return True

        def dfs(i,j,s):
            if not isCellPosValid(i,j):
                return 0
            if grid[i][j] == 0:
                return 0
            if (i,j) in visited:
                return 0
            visited.add((i,j))
            if (i,j) in s:
                return 0
            s.add((i,j))
            r = 0
            for k,l in [[-1,0],[1,0],[0,-1],[0,1]]:
                r += dfs(i+k,j+l,s)
            return r + 1

        id = 1
        m = 1
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    s = set()
                    r = dfs(i,j,s)
                    for k,l in s:
                        g[k][l] = (r, id)
                    m = max(m,r)
                elif grid[i][j] == 0:
                    g[i][j] = (0, id)
                id += 1
        
        print(g)
        
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 0:
                    r = 1
                    s = set()
                    for k,l in [[-1,0],[1,0],[0,-1],[0,1]]:
                        if isCellPosValid(i+k,j+l) and g[i+k][j+l][1] not in s:
                            r += g[i+k][j+l][0]
                            s.add(g[i+k][j+l][1])
                    m = max(m, r)
        return m


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