题目描述

Consider $n$ distinct points on a plane.Two points from that set are said to be friends, when there exists a rectangle with sides parallel to coordinate axes thatcontains those two points and doesn't contain any other point from the given set. A rectangle is said to contain a point if the point lies within the rectangle or on its border.

How many pairs of friends are there among the given points?

求这样的点对个数：以两点连线为对角线的矩形内不存在其他点（也不能在边界上）。

输入格式

The first line of the input file contains an integer $n$ .
The next n lines contain two integers each, the coordinates of the given points. The coordinates don't exceed $10^9$ by absolute value.

输出格式

Output one integer number — the sought number of pairs of friends.

5
0 0
0 2
2 0
2 2
1 1

8

数据规模与约定

对于 $100\%$ 的数据，$1 \le n \le 10^5$ 。