Cycle Detection in a Road Network

You are given an undirected graph representing a road network of villages. The graph contains n villages and m bidirectional roads connecting pairs of villages. A cycle in this context is defined as a sequence of roads:

\( (v_1, v_2), (v_2, v_3), \ldots, (v_{k-1}, v_k), (v_k, v_1) \)

where all \(v_i\) (\(1 \leq i \leq k\)) are distinct and \(k \ge 3\). Your task is to determine whether the road network contains at least one cycle.

If there is a cycle, print YES; otherwise, print NO.

inputFormat

The input is read from stdin and has the following format:

1. The first line contains two integers \(n\) and \(m\) representing the number of villages (nodes) and the number of roads (edges), respectively.
2. The next \(m\) lines each contain two integers \(u\) and \(v\) representing a bidirectional road between villages \(u\) and \(v\).

outputFormat

Print a single line to stdout containing YES if there exists a cycle in the network, or NO otherwise.

## sample

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

YES

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