<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:
        parent = {}
        sizeCC = {}
        n, m = len(grid), len(grid[0])
        for i in range(n):
            for j in range(m):
                if grid[i][j] == 1:
                    parent[(i, j)] = (i,j)
                    sizeCC[(i, j)] = 1

        
        def find(p):
            root = p
            while root!=parent[root]:
                root = parent[root]
            
            while p!=root:
                n = parent[p]
                parent[p] = root
                p = n
            
            return root
        
        def union(p, q):
            root1 = find(p)
            root2 = find(q)
            
            if root1 == root2:
                return
            
            parent[root2] = root1
            
            sizeCC[root1]+=sizeCC[root2]
            sizeCC.pop(root2)
        
        def valid(a):
            return 0<=a[0]<n and 0<=a[1]<m
        
        steps = [[-1, 0], [0, -1], [1, 0], [0, 1]]
        for i in range(n):
            for j in range(m):
                if grid[i][j] == 1:
                    for dx, dy in steps:
                        x, y = i+dx, j+dy
                        if valid((x, y)) and grid[x][y]==1:
                            union((i, j), (x, y))
                    
        if not sizeCC.values():
            return 1
        
        maximum = max(sizeCC.values())
        for i in range(n):
            for j in range(m):
                if grid[i][j] == 0:
                    s = 1
                    found = set()
                    for dx, dy in steps:
                        x, y = i+dx, j+dy
                        if valid((x, y)) and grid[x][y] == 1:
                            p = find((x, y))
                            if p not in found:
                                s+=sizeCC[p]
                                found.add(p)
                   
                    maximum = max(s, maximum)
        
        return maximum
                    
            
            
        
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