Given an directed graph without self-loop, determine whether this graph is a directed acyclic graph (DAG).
### Input
- The first line contains two integers $n,m$.
- The next $m$ lines, each line contains two integers $u, v$ an edge directed from $u$ to $v$.
### Output
- Print `YES` if the given graph is an DAG, otherwise print `NO`.
### Constraints
- $1 \le n,m \le 10^5$.
- $1 \le u,v\le n$.
### Example
Input:
```
3 3
1 2
2 3
1 3
```
Output:
```
YES
```