<p>There are <code>n</code> servers numbered from <code>0</code> to <code>n - 1</code> connected by undirected server-to-server <code>connections</code> forming a network where <code>connections[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> represents a connection between servers <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>. Any server can reach other servers directly or indirectly through the network.</p>

<p>A <em>critical connection</em> is a connection that, if removed, will make some servers unable to reach some other server.</p>

<p>Return all critical connections in the network in any order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/09/03/1537_ex1_2.png" style="width: 198px; height: 248px;" />
<pre>
<strong>Input:</strong> n = 4, connections = [[0,1],[1,2],[2,0],[1,3]]
<strong>Output:</strong> [[1,3]]
<strong>Explanation:</strong> [[3,1]] is also accepted.
</pre>

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

<pre>
<strong>Input:</strong> n = 2, connections = [[0,1]]
<strong>Output:</strong> [[0,1]]
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>n - 1 &lt;= connections.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>There are no repeated connections.</li>
</ul>

from collections import defaultdict
from typing import List, Set, Tuple
from collections import namedtuple

Edge = namedtuple('Edge', ['u', 'v'])

class Solution:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
        graph = defaultdict(list)
        
        for x, y in connections:
            graph[x].append(y)
            graph[y].append(x)
        
        visited: Set[int] = set()
        low: List[int] = [0] * n
        disc: List[int] = [0] * n
        res: List[Edge] = []
        
        def dfs(node: int, parent: int, timer: int) -> int:
            visited.add(node)
            low[node] = disc[node] = timer
            timer += 1
            
            for neigh in graph[node]:
                if neigh == parent:
                    continue
                if neigh not in visited:
                    timer = dfs(neigh, node, timer)
                    
                    if low[neigh] > disc[node]:
                        res.append(Edge(node, neigh))
                    
                low[node] = min(low[node], low[neigh])
            
            return timer
        
        timer = 0
        for i in range(n):
            if i not in visited:
                timer = dfs(i, -1, timer)
        
        return [list(edge) for edge in res]
85703