Graph Connectivity Check

You are given an undirected graph with n nodes and m edges. Your task is to determine whether the graph is connected, i.e. there is a path between every pair of distinct nodes.

The input will begin with two integers n and m. Then, m lines follow, each containing two integers u and v which represent an edge connecting node u and node v. If the graph is connected, print YES, otherwise print NO.

Note: If there is only one node and no edges, the graph is trivially connected.

The formula for connectivity is not explicitly needed here, but you may refer to the formal definition: A graph G is connected if for every pair of vertices u and v, there exists a path between u and v. In LaTeX, this is written as:

\(\forall u,v \in V, \ \exists \text{ a path } u \rightarrow v\)

inputFormat

The first line of input contains two space-separated integers n and m, representing the number of nodes and edges respectively. The next m lines each contain two integers u and v, denoting an edge between nodes u and v.

It is guaranteed that 1 ≤ n ≤ 10⁵ and 0 ≤ m ≤ 10⁵.

outputFormat

Output a single line containing YES if the graph is connected, otherwise output NO.

## sample

4 2
1 2
3 4

NO

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