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Gini Stuðull

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The Gini coefficient in different countries
In the year 1912 the sociologist and statistician Corrado Gini published a paper titled “Variability and Mutability”. In it he introduces the Gini coefficient. The purpose of the coefficient is to measure inequality in distributions and is often used to measure income inequality. The coefficient takes a value between $0$ and $1$, where $0$ denotes perfect equality and $1$ complete inequality. As an example the Gini coefficient of Iceland is $0.256$ and the Gini coefficient of the US is $0.415$.
To calculate the coefficient for a group of people, the income of everyone in that group has to be known. If $y_1, y_2, \ldots , y_ n$ ($y_ i > 0$ for all $i$) denote the incomes of $n$ individuals the Gini coefficient of the group can be calculated using the formula: \[ G = \dfrac { \sum \limits _{i=1}^ n \sum \limits _{j=1}^ n \lvert y_ i - y_ j \rvert }{ 2 \sum \limits _{i=1}^ n \sum \limits _{j=1}^ n y_ i } \]

Here $\lvert x\rvert $ denotes the absolute value of $x$: $\lvert x\rvert = x$ if $x \geq 0$, but $\lvert x\rvert = -x$ if $x < 0$.

Input

The first line of the input contains one integer $n$, the number of individuals in the group. Then there will be $n$ lines, one for each individual in the group, each containing an integer $0 < y_ i \leq 10^5$, the income of the $i$-th individual.

Output

Output the Gini coefficient for the group. The output is considered correct if the relative or absolute error from the correct answer does not exceed $10^{-6}$. This means it does not matter how many significant digits the answer has as long as it’s accurate enough.

Scoring

Group

Points

Constraints

1

50

$n \leq 10^3$

2

50

$n \leq 10^5$

Sample Input 1 Sample Output 1
5
100
100
100
100
100
0.00000000000000000
Sample Input 2 Sample Output 2
5
400
100
300
200
500
0.26666666666666666
Sample Input 3 Sample Output 3
10
1
1
1
1
10000
1
1
1
1
1
0.89910080927165548
CPU Time limit 1 second
Memory limit 1024 MB
Languages English, Íslenska
Author
Garðar Andri Sigurðsson
Source Forritunarkeppni Framhaldsskólanna 2020
License Creative Commons License (cc by-sa)

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