You are given a list of points on a coordinate plane. We need you find the convex hull formed by these points. The convex hull of a set X of points in the Euclidean plane is the smallest convex set that contains X. For instance: when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X. If a point lies on edge, it's included.

The points are presented as a list of coordinates [x, y] in which x and y are integers. The result returns as a sequence of indexes of points in the given list; points lie on the convex hull in clockwise order (see the picture). The sequence starts from the bottom leftmost point. Remember: You should return a list of indexes--not the points themselves.

**
Input:
**
A list of coordinates. Each coordinate is a list of two integers.

**
Output:
**
The list of indexes of coordinates from the given list.

**
Example:
**

checkio([[7, 6], [8, 4], [7, 2], [3, 2], [1, 6], [1, 8], [4, 9]]) == [4, 5, 6, 0, 1, 2, 3] checkio([[3, 8], [1, 6], [6, 2], [7, 6], [5, 5], [8, 4], [6, 8]]) == [1, 0, 6, 3, 5, 2]

**
How it is used:
**
Convex hulls have practical applications in pattern recognition, image processing,
statistics, GIS and static code analysis by abstract interpretation.
The concept also serves as a tool and a building block for a number of other computational-geometric algorithms
such as the rotating calipers method for computing the width and diameter of a point set.

**
Precondition:
**

2 < len(coordinates) < 10

all(0 < x < 10 and 0 < x < 10 for x, y in coordinates)

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CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

checkio --domain=py config --key=

Sync solutions into your local folder

checkio sync

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin

checkio install-plugin --ff

checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.