<p>You are given an <code>m x n</code> binary matrix <code>grid</code>, where <code>0</code> represents a sea cell and <code>1</code> represents a land cell.</p>

<p>A <strong>move</strong> consists of walking from one land cell to another adjacent (<strong>4-directionally</strong>) land cell or walking off the boundary of the <code>grid</code>.</p>

<p>Return <em>the number of land cells in</em> <code>grid</code> <em>for which we cannot walk off the boundary of the grid in any number of <strong>moves</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/enclaves1.jpg" style="width: 333px; height: 333px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,0,0],[1,0,1,0],[0,1,1,0],[0,0,0,0]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are three 1s that are enclosed by 0s, and one 1 that is not enclosed because its on the boundary.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/enclaves2.jpg" style="width: 333px; height: 333px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,0,1,0],[0,0,1,0],[0,0,0,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> All 1s are either on the boundary or can reach the boundary.
</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;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class DSU:
    def __init__(self,n):
        self.par = list(range(n))
        self.size = [1] * n

    def find(self, node):
        if node != self.par[node]:
            self.par[node] = self.find(self.par[node])
        return self.par[node]
    
    def union(self, u, v):
        up = self.find(u)
        vp = self.find(v)
        if up == vp: return
        if self.size[up] < self.size[vp]:
            up, vp = vp, up
        self.size[up] += self.size[vp]
        self.par[vp] = up
class Solution:
    def numEnclaves(self, grid: List[List[int]]) -> int:
        n,m = len(grid), len(grid[0])
        def isBorder(num):
            if 0 <= num < m or (n-1)*m <= num < n*m:
                return True
            return num%m == 0 or num%m == m-1
        dsu = DSU(n*m)
        for i in range(m):
            dsu.size[i] = 1e8
            dsu.size[i+(n-1)*m] = 1e8
        for j in range(n):
            dsu.size[j*m] = 1e8
            dsu.size[(j+1)*m-1] = 1e8
        for i in range(1,n-1):
            for j in range(1,m-1):
                if grid[i][j] == 0: continue
                for di,dj in [[0,1],[1,0],[-1,0],[0,-1]]:
                    ni,nj = i+di, j+dj
                    if 0<=ni<n and 0<=nj<m and grid[ni][nj] == 1:
                        dsu.union(ni*m+nj,i*m+j)
        cnt = 0
        for i in range(n):
            for j in range(m):
                if grid[i][j] == 0: continue
                if not isBorder(dsu.find(i*m+j)):
                    cnt += 1
        return cnt
        
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