Good Triangle

You are given $n$ distinct points on the two dimensional plane.

We define the distance between two points $P=(x\_1, y\_1)$ and $Q=(x\_2, y\_2)$ as $d(P, Q)=|x\_1-x\_2|+|y\_1-y\_2|$.

Let's say that three distinct points $U, V, W$ form a good triangle if there exists a point $T$ such that $d(U, T)=d(V, T)=d(W, T)$. Note that $T$ does not have to be a lattice point.

Find the number of good triangles that can be formed by the given points.

The first line of input contains $N$.

The $i$-th line of the next $N$ lines contains two space-separated integers $x\_i, y\_i$, meaning that the coordinate of the $i$-th point is $(x\_i, y\_i)$.

Print one integer, the number of good triangles that can be formed by the given points.

• $3 \leq N \leq 500\\,000$
• $-10^9 \leq x\_i, y\_i \leq 10^9$ ($1 \leq i \leq N$)
• $(x\_i, y\_i) \neq (x\_j, y\_j)$ if $i\ne j$ ($1 \leq i, j \leq N$)
• All values in the input are integers.