You Never Learned Geometry and Vectors?

Minwoo is a student who entered in 2022. When the 2022 CSAT math exam introduced elective subjects, Minwoo chose Calculus and never learned the beauty of geometry and vectors. Having taught himself geometry and vectors, he wants to show their beauty through the 2023 APC.

The dot product of two vectors $v_{1}=\left( x_{1},y_{1} \right)$ and $v_{2}=\left( x_{2},y_{2} \right)$ in the 2D plane is defined as follows.

$v_{1}\cdot v_{2}=x_{1}x_{2}+y_{1}y_{2}$

If the dot product of two vectors is $0$, the two vectors are perpendicular on the 2D plane.

Given $N$ two-dimensional vectors, count the number of ordered pairs $(i,j)$ where $1\leq i<j\leq N$ and vectors $v_{i}$ and $v_{j}$ are perpendicular.

The first line contains $N$. ($1\leq N\leq 200000$)

From the second line onward, the next $N$ lines each contain $x_{i}$ and $y_{i}$, separated by a space, for vector $v_{i}=(x_{i},y_{i})$. ($-10^{9}\leq x_{i},y_{i}\leq 10^{9}$)

All values in the input are integers.

For integers $i$ and $j$ satisfying $1\leq i<j\leq N$, print the number of ordered pairs $(i,j)$ where vectors $v_{i}$ and $v_{j}$ are perpendicular to each other.