<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)
        ds = DisjointSet(n*n)
        ans = 0

        for i in range(n):
            for j in range(n):
                if grid[i][j] == 0:
                    continue
                delRow = [-1,0,1,0]
                delCol = [0,-1,0,1]
                for k in range(4):
                    r = i + delRow[k]
                    c = j + delCol[k]

                    if r >= 0 and r < n and c >= 0 and c < n and grid[r][c] == 1:
                        ds.unionBySize(i*n+j,r*n+c)

        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1:
                    continue

                delRow = [-1,0,1,0]
                delCol = [0,-1,0,1]
                components = []

                for k in range(4):
                    r = i + delRow[k]
                    c = j + delCol[k]

                    if r >= 0 and r < n and c >= 0 and c < n and grid[r][c] == 1:
                        components.append(ds.findPar(r*n+c))

                sizeTotal = 0
                for it in set(components):
                    sizeTotal += ds.size[it]

                ans = max(sizeTotal+1,ans)

        for i in range(n*n):
            ans = max(ans,ds.size[ds.findPar(i)])

        return ans

class DisjointSet:
    def __init__(self, V):
        self.size = [1]*V
        self.parent = {i: i for i in range(V)}

    def findPar(self, node):
        if self.parent[node] == node:
            return node

        self.parent[node] = self.findPar(self.parent[node])
        return self.parent[node]

    def unionBySize(self, u, v):
        ulp_u = self.findPar(u)
        ulp_v = self.findPar(v)

        if ulp_u == ulp_v:
            return

        if self.size[ulp_u] < self.size[ulp_v]:
            self.parent[ulp_u] = ulp_v
            self.size[ulp_v] += self.size[ulp_u]
        else:
            self.parent[ulp_v] = ulp_u
            self.size[ulp_u] += self.size[ulp_v]




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