Problem6314--ABC231 —— D - Neighbors

6314: ABC231 —— D - Neighbors

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

Determine whether there is a way to line up $N$ people, numbered $1$ to $N$, in a row side by side to satisfy all of the $M$ conditions in the following format.
  • Condition: Person $A_i$ and Person $B_i$ are adjacent.

Input

Input is given from Standard Input in the following format:
$N\ M$
$A_1\ B_1$
$\vdots$
$A_M\ B_M$

Output

If there is a way to line up people to satisfy the conditions, print Yes; if not, print No.

Constraints

$2≤N≤10^5$
$0 \leq M \leq 10^5$
$1\leq A_i < B_i \leq N$
All pairs $(A_i,B_i)$ are distinct.

Sample 1 Input

4 2
1 3
2 3

Sample 1 Output

Yes
One way to satisfy all the conditions is to line them up in the order $4,1,3,2$.

Sample 2 Input

4 3
1 4
2 4
3 4

Sample 2 Output

No
There is no way to line them up to satisfy all the conditions.

Source/Category

AtCoder_ABC 100.231.ABC231