<p>You are given an <code>m x n</code> binary grid <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water. An <strong>island</strong> is a maximal <strong>4-directionally</strong> (horizontal or vertical) connected group of <code>1</code>&#39;s.</p>

<p>The grid is said to be <strong>connected</strong> if we have <strong>exactly one island</strong>, otherwise is said <strong>disconnected</strong>.</p>

<p>In one day, we are allowed to change <strong>any </strong>single land cell <code>(1)</code> into a water cell <code>(0)</code>.</p>

<p>Return <em>the minimum number of days to disconnect the grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]

<strong>Output:</strong> 2
<strong>Explanation:</strong> We need at least 2 days to get a disconnected grid.
Change land grid[1][1] and grid[0][2] to water and get 2 disconnected island.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land2.jpg" style="width: 404px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [[1,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Grid of full water is also disconnected ([[1,1]] -&gt; [[0,0]]), 0 islands.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution:
    def get_neighbours(self, grid: list[list[int]], i,j) -> int:
        result = []
        for di,dj in [(-1,0),(1,0),(0,1),(0,-1)]:
            ni = i + di
            nj = j + dj
            if 0<=ni<len(grid) and 0<=nj<len(grid[0]) and grid[ni][nj]:
                result.append((ni,nj))
        return result

    def minDays(self, grid: List[List[int]]) -> int:
        def get_land(grid):
            for i in range(rows):
                for j in range(cols):
                    if grid[i][j]:
                        return i,j
            
            return None, None

        def get_land_size(grid, i,j):
            queue = [(i,j)]
            visited = set()
            while queue:
                cur_i, cur_j = queue.pop()
                if (cur_i, cur_j) in visited:
                    continue
                
                visited.add((cur_i, cur_j))
                neighbours = self.get_neighbours(grid, cur_i, cur_j)

                for ni, nj in neighbours:
                    queue.append((ni, nj))

            return len(visited)


        count = 0
        rows = len(grid)
        cols = len(grid[0])
        land_count = sum([sum(row) for row in grid])
        
        i, j = get_land(grid)
        
        if i is None:
            return 0
        
        land_size = get_land_size(grid, i,j)
        if land_size<land_count:
            return 0

        for row in range(rows):
            for col  in range(cols):
                if not grid[row][col]:
                    continue    
                grid[row][col] = 0
                i, j = get_land(grid)
                if i is None:
                    return 1
                land_size = get_land_size(grid, i,j)
                if land_size<land_count-1:
                    return 1
                grid[row][col] = 1
        return 2
       
        

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