<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:
        
        def get_travel(r, c):
            return [(r - 1, c), (r + 1, c), (r, c+1), (r, c - 1)]

        def is_valid(r, c):
            return r >= 0 and c >=0 and r < len(grid) and c < len(grid[0])
        
        # label all islands
        #coor, did_change, max

        counter = 2

        island_size = {}
        def dfs(r, c):
            if not is_valid(r, c):
                return 0
            if grid[r][c] !=1:
                return 0

            grid[r][c] = counter
            total = 0
            for new_r, new_c in get_travel(r, c):
                total += dfs(new_r, new_c)
            
            return total + 1

        for r, row in enumerate(grid):
            for c, column in enumerate(grid[0]):
                if grid[r][c] == 1:
                    island_size[counter] = dfs(r, c)
                    counter += 1
        print(grid)
        print(island_size)
        cur_max = 0
    
        for r, row in enumerate(grid):
            for c, column in enumerate(grid[0]):
                if grid[r][c] == 0:
                    touching = set()
                    for new_r, new_c in get_travel(r, c):
                        if not is_valid(new_r, new_c):
                            continue
                        print(grid[new_r][new_c])
                        if grid[new_r][new_c] > 1 and grid[new_r][new_c] not in touching:
                            touching.add(grid[new_r][new_c])

                    all_touching = 0
                    for touch in touching:
                        all_touching += island_size[touch]
                    cur_max = max(cur_max, all_touching + 1)


        if cur_max == 0:
            return island_size[max(island_size, key=island_size.get)]
        return cur_max
        


            

            
            
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