Sgu512 Friendly Points

时间限制:5s      空间限制:128MB

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 that contains 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,1<=N<=100 000.

The next n lines contain two integers each, the coordinates of the given points. The coordinates don't exceed 109 by absolute value.


输出格式

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


样例输入

5
0 0
0 2
2 0
2 2
1 1


样例输出

8

提示

没有写明提示


题目来源

没有写明来源