<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 UnionFind:
    def __init__(self,n):
        self.par = {}
        self.size = {}
        
        for i in range(n):
            self.par[i] = i
            self.size[i] = 1
    
    def find(self,n):
        if self.par[n] == n:
            return self.par[n]
        self.par[n] = self.find(self.par[n])
        return self.par[n]
        
    def union(self,a,b):
        p1,p2 = self.find(a), self.find(b)
        if p1 == p2:
            return
        if self.size[p1] > self.size[p2]:
            self.par[p2] = p1
            self.size[p1] += self.size[p2]
        else:
            self.par[p1] = p2
            self.size[p2] += self.size[p1]

class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        def isvalid(i,j):
            return 0 <= i < n and 0 <= j < n 

        n = len(grid)
        uf = UnionFind(n*n)

        for i in range(n):
            for j in range(n):
                if grid[i][j] == 1:
                    dr = [0 , 1 , 0 , - 1, 0]
                    for x in range(4):
                        nr,nc = i + dr[x], j + dr[x+1]
                        if isvalid(nr,nc) and grid[nr][nc]:
                            curr = i*n + j
                            newc = nr * n + nc
                            uf.union(curr,newc)
        print(uf.size)
        ans = 0
        for i in range(n):
            for j in range(n):
                if grid[i][j] == 0:
                    vi= set()
                    res = 1
                    dr = [0 , 1 , 0 , - 1, 0]
                    for x in range(4):
                        nr,nc = i + dr[x], j + dr[x+1]
                        if isvalid(nr,nc) and grid[nr][nc]:                            
                            newc = nr * n + nc
                            root = uf.find(newc)
                            if root not in vi:
                                res += uf.size[root]
                                vi.add(root)
                    ans = max(ans,res)
        return ans if ans!=0 else n*n

            



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