Detect Cyclic Dependencies in a Directed Graph

You are given a directed graph with \(N\) vertices and \(M\) edges. Your task is to determine whether the graph contains a cycle. If the graph has at least one cycle, print CYCLE; otherwise, print NO CYCLE. This problem can be solved using topological sorting techniques (such as Kahn's algorithm) which check if every vertex is visited in the ordering.

Example:

Input:
3 3
1 2
2 3
3 1
Output:
CYCLE

In the above example, the edge sequence (1,2), (2,3), (3,1) forms a cycle. In contrast, if the input graph is acyclic, the output should be NO CYCLE.

inputFormat

The first line contains two integers (N) and (M) — the number of vertices and edges respectively. Each of the next (M) lines contains two integers (u) and (v), representing a directed edge from vertex (u) to vertex (v).

outputFormat

Print a single line: CYCLE if the graph contains at least one cycle, or NO CYCLE if it is acyclic.## sample

3 3
1 2
2 3
3 1

CYCLE