Cycle Detection in a Directed Graph

You are given a directed graph with (n) nodes (numbered from 0 to (n-1)) and (m) directed edges. Your task is to determine whether the graph contains a cycle. A cycle is a path that starts and ends at the same vertex and contains at least one edge. The graph is provided via standard input (stdin), and your program should output the result to standard output (stdout).

inputFormat

The first line contains two integers (n) and (m), representing the number of nodes and edges respectively. Each of the following (m) lines contains two integers (u) and (v), indicating a directed edge from node (u) to node (v).

outputFormat

Output (True) if the graph contains a cycle; otherwise, output (False).## sample

3 3
0 1
1 2
2 0

True