### 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.

### 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`.

### 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.

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.