In example 1 how 11 came? please anyone explain

I calculated permutation and all but i am not getting how to calculate this 11 Please Help.
Single Lane Highway
Problem Description
Certain number of cars are passing a single lane road. Speeds of all cars vary. It is easy to see, that depending on the speeds of the cars various groups will be formed.

Being a single lane road passing/overtaking is not allowed. Given speeds of cars, calculate how many groups can be formed if all possible permutations are taken into account. Refer example1 for better understanding.

Print number of groups divided by the number of permutations.

Constraints
0 <= N < 10 ^ 5

0 <= speed of individual vehicle < 10 ^ 9

Input
First line contains an integer N, which denotes the number of vehicles

Second line contains N space separated integers which denotes the speed of individual vehicle.

Output
Print number of groups divided by the number of permutations rounded upto 6 decimal places.

Time Limit
Examples
Example 1

Input

3

10 20 30

Output

1.833333

Explanation:

So all possible permutations are:

{10 20 30}

{10 30 20}

{20} {10 30}

{20 30} {10}

{30} {10 20}

{30 20} {10}

So here there are total 6 permutations, and total number of groups are 11.

So, output is 11/6 = 1.833333

Example 2

Input

4

56 78 13 92

Output

2.083333

Explanation:

So here there are total 24 permutations,

For example:

{56 78 13 92}

{92} {13 78 56}

{56} {13 92 78}

{78 92} {13 56}

.

.

So on and so forth. The total number of groups are 50.

So, the output is 50/24 = 2.083333

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Author: Abhinav Shukla

Integrating TeX into a Java desktop application

Looking to integrate TeX equations in a TeX-agnostic fashion, suitable for either ConTeXt or LaTeX, into a Java-based desktop Markdown editor. The possibilities are numerous, but I’m not sure what approach to take.

JMathTex outputs to MathML, which must be transformed. JEuclid can transform MathML to BufferedImages (not 100% sure). Neither are JDK 14-friendly and may be too slow to render in real-time. I haven’t looked because I read that they didn’t work with Java 9 (without porting effort), much less 14. Also, the licensing isn’t LGPL, which probably won’t work with the MIT licensing.

The NTS library is reported to compile gentle.tex in about 3 seconds. The spin-off project, εχTEX improves upon NTS, but I don’t know to what extent.

Java LaTeX Report requires a TeX engine.

Yet another possibility is to try JavaTex or rework the project using web2java to transpile WEB files into Java files.

JLaTeXMath does an exceptional job at rendering, though investigation would be required to see if it can perform real-time renders, output as SVG, or otherwise determine if it can integrate with FlyingSaucer.

The HTML preview panel uses FlyingSaucer. The SVG documents are rendered using SVG Salamander. If it was possible to go from TeX to SVG, that could work quite handily, architecturally. Some documentation stated FlyingSaucer can also render MathML, but I suspect the doc is wrong. FlyingSaucer doesn’t integrate with JavaScript. For that I’d have to add a JavaScript Engine.

If a JavaScript Engine is necessary, then using KaTeX may be an option.

Still another possibility is the TeX to MathML service. This is written in Java, but the source code is not available anywhere. I’ve reached out to some people involved in the project.

For native speeds, there may be a (cross-platform?) C-based TeX engine that can generate MathML or SVG from a TeX input. If so, it may be possible to integrate with the JNI.

Here’s a demo video of the app, to give you an idea of what is needed:

The goal is to produce real-time rendering of math, ideally in pure Java (no JavaScript).

What approach would you take and what do you see as its benefits and drawbacks?

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Author: Dave Jarvis