<p>Given an <code>m x n</code> <code>board</code>&nbsp;of characters and a list of strings <code>words</code>, return <em>all words on the board</em>.</p>

<p>Each word must be constructed from letters of sequentially adjacent cells, where <strong>adjacent cells</strong> are horizontally or vertically neighboring. The same letter cell may not be used more than once in a word.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/07/search1.jpg" style="width: 322px; height: 322px;" />
<pre>
<strong>Input:</strong> board = [[&quot;o&quot;,&quot;a&quot;,&quot;a&quot;,&quot;n&quot;],[&quot;e&quot;,&quot;t&quot;,&quot;a&quot;,&quot;e&quot;],[&quot;i&quot;,&quot;h&quot;,&quot;k&quot;,&quot;r&quot;],[&quot;i&quot;,&quot;f&quot;,&quot;l&quot;,&quot;v&quot;]], words = [&quot;oath&quot;,&quot;pea&quot;,&quot;eat&quot;,&quot;rain&quot;]
<strong>Output:</strong> [&quot;eat&quot;,&quot;oath&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/07/search2.jpg" style="width: 162px; height: 162px;" />
<pre>
<strong>Input:</strong> board = [[&quot;a&quot;,&quot;b&quot;],[&quot;c&quot;,&quot;d&quot;]], words = [&quot;abcb&quot;]
<strong>Output:</strong> []
</pre>

<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;= 12</code></li>
	<li><code>board[i][j]</code> is a lowercase English letter.</li>
	<li><code>1 &lt;= words.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words[i].length &lt;= 10</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>words</code> are unique.</li>
</ul>

class Solution:
    def findWords(self, board: List[List[str]], words: List[str]) -> List[str]:
        root = Node()
        for w in words: root.insert(w)

        res = set()
        M, N = len(board), len(board[0])
        dirs = [[0,1],[1,0],[0,-1],[-1,0]]

        def dfs(r, c, node):
            if r not in range(M) or c not in range(N): return
            ch = board[r][c]
            if ch == None or ch not in node.next: return
            board[r][c] = None
            node = node.next[ch]
            if node.end:
                res.add(node.word)
                root.remove(root, node.word)
            for dr, dc in dirs:
                dfs(r+dr, c+dc, node)
            board[r][c] = ch
        
        for r in range(M):
            for c in range(N):
                dfs(r, c, root)
        
        return list(res)

class Node:
    def __init__(self, c=''):
        self.c = c
        self.next = {}
        self.word = ''
        self.end = False
    
    def insert(self, word: str) -> None:
        cur = self
        for c in word:
            if c not in cur.next: cur.next[c] = Node(c)
            cur = cur.next[c]
        cur.word = word
        cur.end = True
    
    def remove(self, node, word: str) -> None:
        if not node.next: return True
        if not word: return False
        c = word[0]
        if c not in node.next: return False
        if self.remove(node.next[c], word[1:]): node.next.pop(c)
        else: return False
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