There are $n$ intersections and $m$ roads connecting them in the city. Your task is to check if it is possible to get from every intersection to every other intersection by roads.

Input

On the first line of the input there is two integers $n$ and $m$: the number of intersections and number of roads. Intersections are numbered $1,2,\ldots,n$.

Then $m$ lines follow, each describing one road. Each line has two integers $a$ and $b$. This means that there is a road connecting intersection $a$ to intersection $b$. All roads are unidirectional.

Output

Print YES if there exists a route from every intersection to every other intersection, or NO otherwise.

If the answer is NO, continue output by printing an example of intersections $a$ and $b$ such that there exists no route from $a$ to $b$.

Limits

• $1 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le a,b \le n$

Example

Input:

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

Output:

NO
4 2