Problem D
Gini Stuðull

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