Given a connected graph $G$ with $n$ vertices and $m$ undirected edges. Count the number of pairs $u, v$ with $u < v$ such that there exists exactly one path from $u$ to $v$. A path is considered valid if each edge and vertex on the path is traversed exactly once.
### Input
- The first line contains two positive integers $n, m$.
- The next $m$ lines, each containing two positive integers $u_i, v_i$ that describe an edge of the graph.
### Output
- Print the answer to the problem.
### Constraints
- $1 \le n,m \le 2 \cdot 10^5.$
### Example
Input
```
5 5
1 2
1 5
3 2
4 5
1 3
```
Output
```
3
```