Given a undirected graph of $n$ vertices and $m$ edges. Determine whether or not this graph is a bipartite graph.
A graph is bipartite if and only if you can color its vertices in 2 different colors such that no 2 adjacent vertices have the same color.
### Input
- The first line contains 2 integers $n, m$.
- The next $m$ lines, each line contains 2 integers $u, v$, there is an edge between $u$ and $v$. It is guaranteed that there is no loop.
### Output
- Print `YES` if the given graph is bipartite, otherwise print `NO`.
### Constraints
- $1 \le n, m \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
5 4
3 1
5 2
1 4
2 3
```
Output:
```
YES
```
