Given $2n+1$ distinct points $(x_i, y_i)$ on a 2D plane.
**Task**: Count the number of points such that if we remove that point, the remaining $2n$ points can be partitioned into $n$ pairs, where each pair shares either the same x-coordinate or the same y-coordinate.
#### Input
- First line contains integer $n$ ($1 \le n \le 10^5$).
- The next $2n+1$ lines each contain two integers $x_i, y_i$ ($0 \le x_i, y_i \le 10^9$).
#### Output
- Print the number of such points.
#### Example
Input:
```
3
0 0
0 1
1 0
1 1
2 2
2 3
3 2
```
Output:
```
2
```
#### Subtasks
- **Subtask 1 (17 points)**: $n \le 8$.
- **Subtask 2 (18 points)**: $n \le 50$.
- **Subtask 3 (25 points)**: $n \le 1000$ and there are at most 2 distinct x-coordinates.
- **Subtask 4 (20 points)**: $n \le 1000$.
- **Subtask 5 (20 points)**: No additional constraints.
