Projected Array

There are $N$ distinct points on a two-dimensional plane. Each point has a different integer from $1$ to $N$ written on it.

Now rotate every point around the origin by a certain angle and project them onto the $x$-axis. Read the points in increasing order of their $x$-coordinates, and the numbers written on them form a sequence of length $N$. However, no two points may have the same $x$-coordinate after rotation. Among the sequences that can be made this way, find the minimum number of inversions.

Here, the number of inversions of a sequence $A_1, A_2, \cdots, A_n$ is the number of pairs $(i, j)$ with $1 \le i < j \le n$ and $A_i > A_j$.

The first line contains the number of points $N$. ($1 \le N \le 2000$)

The next $N$ lines each contain two integers $x_i$ and $y_i$ separated by a space, the coordinates of the point that has the integer $i$ written on it. ($1 \le i \le N$; $-10^9 \le x_i, y_i \le 10^9$)

On the first line, print the minimum possible number of inversions.