Unicyclic Components

AtCoder

IDabc292_d

Time2000ms

Memory256MB

Difficulty—

You are given an undirected graph with $N$ vertices numbered $1$ to $N$ and $M$ edges numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$. Determine whether every connected component in this graph satisfies the following condition. * The connected component has the same number of vertices and edges. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq M \leq 2 \times 10^5$ * $1 \leq u_i \leq v_i \leq N$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $u_1$ $v_1$ $\vdots$ $u_M$ $v_M$ [samples] ## Notes An **undirected graph** is a graph with edges without direction. A **subgraph** of a graph is a graph formed from a subset of vertices and edges of that graph. A graph is **connected** when one can travel between every pair of vertices in the graph via edges. A **connected component** is a connected subgraph that is not part of any larger connected subgraph.

Samples

Input #1

Output #1

Yes

The graph has a connected component formed from just vertex $1$, and another formed from vertices $2$ and $3$.  
The former has one edge (edge $2$), and the latter has two edges (edges $1$ and $3$), satisfying the condition.

Input #2

Output #2

Yes

Input #3

Output #3

No

API Response (JSON)

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