<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 minDays(self, grid: List[List[int]]) -> int:
        m,n=len(grid),len(grid[0])
        def isGate(y,x):
            if grid[y][x]==0:
                return False
            if grid[y][x]<0:
                return True
            outs=connectors=0
            for yy,xx in [(y+1,x),(y-1,x),(y,x+1),(y,x-1)]:
                if 0<=yy<m and 0<=xx<n and grid[yy][xx]!=0: 
                    outs+=1
            for yy,xx in [(y+1,x+1),(y+1,x-1),(y-1,x-1),(y-1,x+1)]:
                if 0<=yy<m and 0<=xx<n and grid[yy][xx]!=0 and grid[yy][x]!=0 and grid[y][xx]!=0:
                    connectors+=1
            res=outs-connectors
            return res>1
        def isNode(y,x):
            return not isGate(y,x)
        self.gatemark,self.nodemark=-1,2
        landfound=False
        def someshit(y,x):
            gcolor=isGate(y,x)
            checkfunc=isGate if gcolor else isNode
            mark=self.gatemark if gcolor else self.nodemark
            if not gcolor:
                nodes.append((y,x))
            grid[y][x]=mark
            stack=[(y,x)]
            adjacents=[]
            while stack:
                y,x=stack.pop()
                if(gcolor):gates.append((y,x))
                for yy,xx in [(y-1,x),(y+1,x),(y,x+1),(y,x-1)]:
                    if 0<=yy<m and 0<=xx<n:
                        if checkfunc(yy,xx):
                            if grid[yy][xx]==1:
                                grid[yy][xx]=mark
                                stack.append((yy,xx))
                        else:
                            if grid[yy][xx]==1:
                                adjacents.append((yy,xx))
            if gcolor:    self.gatemark-=1
            else:         self.nodemark+=1
            for y,x in adjacents:
                if grid[y][x]!=1:
                    continue
                someshit(y,x)
        onetiler=False
        gates=[]
        nodes=[]
        for i in range(m):
            for j in range(n):
                if grid[i][j]==1:
                    if landfound:
                        return 0
                    landfound=True
                    if all(0<=yy<m and 0<=xx<n and grid[yy][xx]==0 for yy,xx in [(i+1,j),(i-1,j),(i,j+1),(i,j-1)]):
                        onetiler=True
                        continue
                    someshit(i,j)
        if onetiler:
            return 1
        if len(nodes)==0:
            return 0
        graph=[[[] for _ in range(n)]for _ in range(m)]
        for y,x in gates:
            seen=set()
            for yy,xx in [(y+1,x),(y-1,x),(y,x+1),(y,x-1)]:
                if 0<=yy<m and 0<=xx<n and grid[yy][xx]!=0:
                    if grid[yy][xx]>0:
                        yy,xx=nodes[grid[yy][xx]-2]
                    if (yy,xx) in seen: continue
                    seen.add((yy,xx))
                    graph[yy][xx].append((y,x))
                    graph[y][x].append((yy,xx))
        for i,(y,x) in enumerate(gates):
            seen=set()
            seen.add((y,x))
            yy,xx=graph[y][x][0]
            seen.add((yy,xx))
            stack=[(yy,xx)]
            while stack:
                yy,xx=stack.pop()
                for yyy,xxx in graph[yy][xx]:
                    if (yyy,xxx) in seen:
                        continue
                    seen.add((yyy,xxx))
                    stack.append((yyy,xxx))
            for yy,xx in graph[y][x]:
                if (yy,xx) not in seen:
                    return 1
        return 2

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