The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
A. Supercentral Point

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne 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.

Input

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.

Output

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

Examples

Input

8

1 1

4 2

3 1

1 2

0 2

0 1

1 0

1 3

Output

2

Input

5

0 0

0 1

1 0

0 -1

-1 0

Output

1

Note

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).

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/03/2022 10:40:49 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|