<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)
        parents = [i for i in range(n*n)]
        size = [1] * (n*n)
        # vis = [[-1]*m for _ in range(n)]

        def findPar(node):
            if parents[node] == node:
                return node
            parents[node] = findPar(parents[node])
            return parents[node]
        
        def unionBySize(u,v):
            ulpar_u = parents[u]
            ulpar_v = parents[v]
            if ulpar_u == ulpar_v:
                return 
            if size[ulpar_u] < size[ulpar_v]:
                parents[ulpar_u] = ulpar_v
                size[ulpar_v] += size[ulpar_u]
            else:
                parents[ulpar_v] = ulpar_u
                size[ulpar_u] += size[ulpar_v]

        for r in range(n):
            for c in range(n):
                if grid[r][c] == 1:
                    for dx, dy in [(0, 1), (1, 0), (0, -1), (-1, 0)]:
                        adjx, adjy = r + dx, c + dy
                        if 0 <= adjx < n and 0 <= adjy < n and grid[adjx][adjy] == 1:
                            currNo = r * n + c
                            adjNo = adjx * n + adjy
                            if findPar(currNo) != findPar(adjNo):
                                unionBySize(currNo, adjNo)

        # print(size)
        maxIslandSize = max(size) 
        for r in range(n):
            for c in range(n):
                if grid[r][c] == 0:
                    seen = set()
                    totalSize = 1 
                    for dx, dy in [(0, 1), (1, 0), (0, -1), (-1, 0)]:
                        adjx, adjy = r + dx, c + dy
                        if 0 <= adjx < n and 0 <= adjy < n and grid[adjx][adjy] == 1:
                            parent = findPar(adjx * n + adjy)
                            if parent not in seen:  
                                totalSize += size[parent]
                                seen.add(parent)
                    maxIslandSize = max(maxIslandSize, totalSize)

        return maxIslandSize
36793