Supercentral Point · Interview Problem

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Codeforces

Easy

Arrays

Geometry

Supercentral Point

Count how many points in a set have at least one point strictly above, below, to the left, and to the right of them.

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CF 165A

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Problem Statement

Problem

You are given $n$ points on a 2D plane. A point is called supercentral if there exists at least one other point:

with the same $x$ coordinate and a larger $y$ coordinate,
with the same $x$ coordinate and a smaller $y$ coordinate,
with the same $y$ coordinate and a larger $x$ coordinate,
with the same $y$ coordinate and a smaller $x$ coordinate.

In other words, a supercentral point must have at least one point in each of the four cardinal directions: up, down, left, and right.

Your task is to determine how many points are supercentral.

Notes

A point does not count itself.
All points are distinct.
Points are considered only by exact coordinate equality on one axis and strict inequality on the other.

Input Format

The first line contains an integer $n$ .
Each of the next $n$ lines contains two integers $x_i$ and $y_i$ , the coordinates of a point.

Output Format

Print a single integer — the number of supercentral points.

Constraints

$1 \le n \le 200$
Coordinates are integers and fit in 32-bit signed range.
All points are distinct.

Examples

Sample cases returned by the problem API.

Example 1

Input

Output

Explanation

Only point $(0,0)$ has a point to the left, right, above, and below it.

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