<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,size):
        self.t_size, self.parent = [1 for _ in range(size)],[-1 for _ in range(size)]
        self.area = 0
        self.size = size
        self.cnt = 0

    def find(self,idx):
        #no path compression
        if self.parent[idx] == -1:
            return idx
        return self.find(self.parent[idx])

    def union(self,n1,n2):
        
        n1,n2 = self.find(n1),self.find(n2)
        if n1 == n2:
            return
        elif self.t_size[n1] > self.t_size[n2]:
            self.parent[n2] = n1
            self.t_size[n1] += self.t_size[n2]
        else:
            self.parent[n1] = n2
            self.t_size[n2] += self.t_size[n1]
        
        self.cnt -= 1
      



class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:

        m,n = len(grid),len(grid[0])
        uf = UnionFind(m*n)
        directions = [(-1,0),(1,0),(0,-1),(0,1)]

        

        #first iterate over every grid and store size
        for x in range(m):
            for y in range(n):
                if grid[x][y] == 1:
                    for dx , dy in directions:
                        n_x, n_y = x + dx, y + dy
                        n_idx = n_x*n + n_y

                        if n_x >= 0 and n_x < m and n_y >= 0 and n_y < n and grid[n_x][n_y] == 1:
                            uf.union(x*n + y, n_idx)
                    
        res = 0

        for i in range(m):
            for j in range(n):
                n_idx = i*n + j
                res = max(res,uf.t_size[uf.find(n_idx)])


        for x in range(m):
            for y in range(n):
                if grid[x][y] == 0:
                    temp = 1
                    used = set()
                    for dx , dy in directions:
                        n_x, n_y = x + dx, y + dy
                        n_idx = n_x*n + n_y
                      
                        if n_x >= 0 and n_x < m and n_y >= 0 and n_y < n and grid[n_x][n_y] == 1:
                            
                            idx = uf.find(n_idx)
                            if idx not in used:
                                used.add(idx)
                                temp += uf.t_size[idx]
                            
            
                    res = max(res,temp)
                    
   
            
       
        return res

        
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