Contest Duration: - (local time) (100 minutes) Back to Home
D - Unicyclic Components /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

このグラフのすべての連結成分が次の条件を満たすかどうかを判定してください。

• その連結成分に含まれる頂点の個数と辺の本数が等しい。

注釈

あるグラフの 部分グラフ とは、元のグラフのいくつかの頂点といくつかの辺を選んでできるグラフのことをいいます。
グラフが 連結 であるとは、グラフに含まれるすべての頂点同士が辺を経由して互いに行き来できることをいいます。

制約

• 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
• 入力はすべて整数

入力

N M
u_1 v_1
\vdots
u_M v_M


出力

すべての連結成分が条件を満たすならば Yes と、そうでなければ No と出力せよ。

入力例 1

3 3
2 3
1 1
2 3


出力例 1

Yes


このグラフには頂点 1 のみからなる連結成分と頂点 2,3 からなる連結成分があります。

入力例 2

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


出力例 2

Yes


入力例 3

13 16
7 9
7 11
3 8
1 13
11 11
6 11
8 13
2 11
3 3
8 12
9 11
1 11
5 13
3 12
6 9
1 10


出力例 3

No


Score : 400 points

Problem Statement

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.

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.

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


Output

If every connected component satisfies the condition, print Yes; otherwise, print No.

Sample Input 1

3 3
2 3
1 1
2 3


Sample 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.

Sample Input 2

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


Sample Output 2

Yes


Sample Input 3

13 16
7 9
7 11
3 8
1 13
11 11
6 11
8 13
2 11
3 3
8 12
9 11
1 11
5 13
3 12
6 9
1 10


Sample Output 3

No