<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:
        ROWS, COLS = len(grid), len(grid[0])  # Corrected ROWS and COLS assignment
        parent = [i for i in range(ROWS*COLS)]
        size = [1] * (ROWS*COLS)

        def find(node):
            p = parent[node]
            while p != parent[p]:
                parent[p] = parent[parent[p]]
                p = parent[p]
            return p

        def union(u, v):
            par_u = find(u)
            par_v = find(v)

            if par_u == par_v:
                return 
            
            if size[par_u] > size[par_v]:
                size[par_u] += size[par_v]
                parent[par_v] = par_u
            else:
                size[par_v] += size[par_u]
                parent[par_u] = par_v
        
        visited = set()
        dirs = [[1, 0], [0, 1], [-1, 0], [0, -1]]

        for r in range(ROWS):
            for c in range(COLS):
                if grid[r][c] == 1:
                    for dr, dc in dirs:
                        nR = r + dr
                        nC = c + dc
                        if nR in range(ROWS) and nC in range(COLS) and grid[nR][nC]:
                            union(r * COLS + c, nR * COLS + nC)
        
        maxi = max(size)

        for r in range(ROWS):
            for c in range(COLS):
                if grid[r][c] == 0:
                    currSize = 1
                    distinctPar = set()
                    for dr, dc in dirs:
                        nR = r + dr
                        nC = c + dc
                        if nR in range(ROWS) and nC in range(COLS) and grid[nR][nC]:
                            cellPar = find(nR * COLS + nC)
                            if cellPar not in distinctPar:
                                currSize += size[cellPar]
                                distinctPar.add(cellPar)
                    maxi = max(maxi, currSize)
        
        return maxi

                    
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