Critical Road Network

You are given a road network connecting n cities with m bidirectional roads. Your task is to determine whether the road network remains connected if any single road is removed. In other words, you need to decide if the network is 2-edge-connected i.e., there is no critical road (bridge) whose removal disconnects the network.

If there exists at least one road whose removal disconnects the network, output NO. Otherwise, output YES.

Note: A bridge in a graph is an edge which, when removed, increases the number of connected components. The algorithm should find bridges using a DFS-based approach. In terms of formula, if \(\text{low}[v] > \text{disc}[u]\) for an edge \((u, v)\), then this edge is a bridge.

inputFormat

The input is given from standard input (stdin) and has the following format:

1. The first line contains two integers n and m separated by a space, where n is the number of cities and m is the number of roads.
2. The next m lines each contain two integers u and v representing a bidirectional road connecting cities u and v.

outputFormat

Output a single line to standard output (stdout) containing YES if the road network remains connected after removing any single road, and NO otherwise.

5 5
1 2
2 3
3 4
4 5
5 1

YES