<p>You are given an <code>m x n</code> matrix <code>board</code> containing <strong>letters</strong> <code>&#39;X&#39;</code> and <code>&#39;O&#39;</code>, <strong>capture regions</strong> that are <strong>surrounded</strong>:</p>

<ul>
	<li><strong>Connect</strong>: A cell is connected to adjacent cells horizontally or vertically.</li>
	<li><strong>Region</strong>: To form a region <strong>connect every</strong> <code>&#39;O&#39;</code> cell.</li>
	<li><strong>Surround</strong>: The region is surrounded with <code>&#39;X&#39;</code> cells if you can <strong>connect the region </strong>with <code>&#39;X&#39;</code> cells and none of the region cells are on the edge of the <code>board</code>.</li>
</ul>

<p>A <strong>surrounded region is captured</strong> by replacing all <code>&#39;O&#39;</code>s with <code>&#39;X&#39;</code>s in the input matrix <code>board</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = [[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;O&quot;,&quot;O&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;X&quot;,&quot;O&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;O&quot;,&quot;X&quot;,&quot;X&quot;]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;X&quot;,&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;O&quot;,&quot;X&quot;,&quot;X&quot;]]</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/19/xogrid.jpg" style="width: 367px; height: 158px;" />
<p>In the above diagram, the bottom region is not captured because it is on the edge of the board and cannot be surrounded.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">board = [[&quot;X&quot;]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[[&quot;X&quot;]]</span></p>
</div>

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

<ul>
	<li><code>m == board.length</code></li>
	<li><code>n == board[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>board[i][j]</code> is <code>&#39;X&#39;</code> or <code>&#39;O&#39;</code>.</li>
</ul>

class UnionFind:
    def __init__(self, n=0):
        self.parent = [None] * (n)
        self.node_count = n
        self.size = [1] * (n) 

    def find(self, x):
        if self.parent[x] is None:
            return x
        self.parent[x] = self.find(self.parent[x])
        return self.parent[x]

    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px == py:
            return 0
        if self.size[px] > self.size[py]:
            self.parent[py] = px
            self.size[px] += self.size[py]
        else:
            self.parent[px] = py
            self.size[py] += self.size[px]
        self.node_count -= 1
        return 1

    def add(self, n):
        self.parent.extend([None] * n)
        self.node_count += n
        self.size.extend([1] * n)

    def is_connected(self):
        return self.node_count == 1

    def roots(self):
        return [i for i, x in enumerate(self.parent) if x is None]

    def __str__(self):
        return f"UnionFind<{self.parent}>"
        
class UnionFindOverSequence():
    def __init__(self, seq=[]):
        self.seq = list(seq)
        self.map = {x: i for i, x in enumerate(self.seq)}
        self._uf = UnionFind(len(self.seq))

    def find(self, x):
        return self.seq[self._uf.find(self.map[x])]

    def union(self, x, y):
        return self._uf.union(self.map[x], self.map[y])

    def parents(self):
        return {x: self.seq[i] for x, i in self.map.items()}

    def roots(self):
         return [self.seq(i) for i in self._uf.roots()]

class Solution:
    def solve(self, board: List[List[str]]) -> None:
        """
        Do not return anything, modify board in-place instead.
        """
        m, n = len(board), len(board[0])
        olist = []
        for i in range(m):
            for j in range(n):
                if board[i][j] == "O":
                    olist.append((i, j))

        uf = UnionFindOverSequence(olist)
        for x, y in olist:
            for ngh in [(x - 1, y), (x, y - 1)]:
                try:
                    uf.union((x, y), ngh)
                except KeyError:
                    pass
        
        taintedset = set()
        for i, j in olist:
            tainted = (i in [0, m - 1] or j in [0, n - 1])
            if tainted:
                taintedset.add(uf.find((i, j)))

        for i, j in olist:
            if uf.find((i, j)) not in taintedset:
                board[i][j] = "X"
        
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