Problem Statement

Given a directed graph with n nodes and m edges, output a topological ordering of the nodes. If the graph contains a cycle, output "CYCLE".

Use Kahn's algorithm with a min-heap for tie-breaking (always process the node with the smallest index first).

Algorithm:

1. Compute in-degrees for all nodes.
2. Initialize a min-heap with all nodes of in-degree 0.
3. Repeatedly extract the smallest node, add to the result, and decrement in-degrees of its neighbors. Push any neighbor whose in-degree drops to 0 into the heap.
4. If the result has fewer than n nodes, a cycle exists.

Function signature:

def topo_sort(n: int, edges: list) -> list | None:
    # edges: list of (u, v) — directed edge from u to v
    # returns sorted order as list, or None if cycle detected

Input Format

Line 1: n m — number of nodes and directed edges
Lines 2..m+1: u v — directed edge from u to v

Output Format

If no cycle: space-separated node indices in topological order
If cycle: CYCLE

Example

Input:

6 6
5 2
5 0
4 0
4 1
2 3
3 1

Output:

4 5 0 2 3 1

Notes

• The min-heap tie-breaking ensures a deterministic, lexicographically smallest valid topological order.
• Node 4 and 5 both have in-degree 0; 4 is processed first (smaller index).
• Topological sort is only possible for Directed Acyclic Graphs (DAGs).