CSES - Intersection Points
  • Time limit: 1.00 s
  • Memory limit: 512 MB
Given $n$ horizontal and vertical line segments, your task is to calculate the number of their intersection points.

You can assume that no parallel line segments intersect, and no endpoint of a line segment is an intersection point.

Input

The first input line has an integer $n$: the number of line segments.

Then there are $n$ lines describing the line segments. Each line has four integers: $x_1$, $y_1$, $x_2$ and $y_2$: a line segment begins at point $(x_1,y_1)$ and ends at point $(x_2,y_2)$.

Output

Print the number of intersection points.

Constraints
  • $1 \le n \le 10^5$
  • $-10^6 \le x_1 \le x_2 \le 10^6$
  • $-10^6 \le y_1 \le y_2 \le 10^6$
  • $(x_1,y_1) \neq (x_2,y_2)$
Example

Input:
3
2 3 7 3
3 1 3 5
6 2 6 6


Output:
2