Count the number of intersections between $n$ line segments on a two-dimensional coordinate grid. All line segments are parallel to either the x-axis or the y-axis. Two segments may have more than one intersections.
### Input
- The first line contains an integer $n$.
- The next $n$ lines each contain four integers $x_1, y_1, x_2, y_2$ representing a line segment with endpoints $(x_1, y_2)$ and $(x_2, y_2)$.
### Output
- Print an integer representing the number of intersections.
### Constraints
- $1 \leq n \leq 2 \times 10^5$.
- $1 \leq x_1, y_1, x_2, y_2 \leq 10^5$.
### Example
Input:
```
4
1 2 4 2
2 3 2 1
4 1 4 4
1 4 2 4
```
Output:
```
2
```
