Jerry is being chased by Tom on a connected graph of $n$ vertices and $m$ edges. Jerry is currently at vertex $a$, and Tom is currently at vertex $b$. They both need $1$ unit of time to run from a vertex to another.
You can choose to stand at a vertex. If Jerry can arrive at your vertex no later than Tom, you can save Jerry.
In how many vertices can you stand in order to save Jerry?
### Input
- The first line contains 2 integers $n, m$.
- The second line contains 2 integers $a, b$.
- The next $m$ lines, each line contains 2 integers $u, v$, there is an edge between $u$ and $v$.
### Output
- Print the number of vertices you can choose to stand at to save Jerry.
### Constraints
- $1 \le n, m \le 10^5$.
- $1 \le u, v,a, b \le n$.
### Example
Input:
```
6 6
3 5
1 2
1 5
2 3
2 4
4 5
4 6
```
Output:
```
2
```
#### **Note**: You can choose to stand at either $2$ or $3$.
