Supercentral Point

题意翻译

在一个平面直角坐标系中，给定$n$个点。求有多少个点满足在它的**正**上方，**正**下方，**正**左方，**正**右方都有点。

题目描述

One day Vasya painted a Cartesian coordinate system on a piece of paper and marked some set of points $ (x_{1},y_{1}),(x_{2},y_{2}),...,(x_{n},y_{n}) $ . Let's define neighbors for some fixed point from the given set $ (x,y) $ : - point $ (x',y') $ is $ (x,y) $ 's right neighbor, if $ x'>x $ and $ y'=y $ - point $ (x',y') $ is $ (x,y) $ 's left neighbor, if $ x'<x $ and $ y'=y $ - point $ (x',y') $ is $ (x,y) $ 's lower neighbor, if $ x'=x $ and $ y'<y $ - point $ (x',y') $ is $ (x,y) $ 's upper neighbor, if $ x'=x $ and $ y'>y $ We'll consider point $ (x,y) $ from the given set supercentral, if it has at least one upper, at least one lower, at least one left and at least one right neighbor among this set's points. Vasya marked quite many points on the paper. Analyzing the picture manually is rather a challenge, so Vasya asked you to help him. Your task is to find the number of supercentral points in the given set.

输入输出格式

输入格式

The first input line contains the only integer $ n $ ( $ 1<=n<=200 $ ) — the number of points in the given set. Next $ n $ lines contain the coordinates of the points written as " $ x $ $ y $ " (without the quotes) ( $ |x|,|y|<=1000 $ ), all coordinates are integers. The numbers in the line are separated by exactly one space. It is guaranteed that all points are different.

输出格式

Print the only number — the number of supercentral points of the given set.

输入输出样例

输入样例 #1

8
1 1
4 2
3 1
1 2
0 2
0 1
1 0
1 3

输出样例 #1

2

输入样例 #2

5
0 0
0 1
1 0
0 -1
-1 0

输出样例 #2

1

说明

In the first sample the supercentral points are only points $ (1,1) $ and $ (1,2) $ . In the second sample there is one supercental point — point $ (0,0) $ .

题意翻译

在一个平面直角坐标系中，给定$n$个点。求有多少个点满足在它的**正**上方，**正**下方，**正**左方，**正**右方都有点。