J. Joyeuse
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

At a grand and dazzling dance party, there are $$$N$$$ guests, each with their own dance skill power $$$a_i$$$.

When two guests pair up on the dance floor, their performance score is equal to the square root of the sum of their skill powers. For example, if one guest has a skill power of $$$4$$$ and another has $$$5$$$, their duet would have a performance score of $$$\sqrt{4 + 5} = 3$$$.

As the host of this vivid celebration, you wish to measure the collective joy — the total performance score of every possible pair of guests dancing together exactly once.

Your task is to determine this total score.

Input

The first line contains a single integer $$$n$$$ ($$$2 \le n \le 200000$$$) — the number of guests.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1\le a_i \le 10^9$$$) — the dancing skill powers of the guests.

Output

A single real number — the total performance score at the party.

The answer is considered correct if the relative error does not exceed $$$10^{-6}$$$.

Example
Input
5
7 3 11 2 17
Output
39.009712
Note

All possible pairs and their performance scores are:

Guest $$$1$$$ and guest $$$2$$$: $$$\sqrt{7+3} \approx 3.162277660$$$

Guest $$$1$$$ and guest $$$3$$$: $$$\sqrt{7+11} \approx 4.242640687$$$

Guest $$$1$$$ and guest $$$4$$$: $$$\sqrt{7+2} = 3$$$

Guest $$$1$$$ and guest $$$5$$$: $$$\sqrt{7+17} \approx 4.898979486$$$

Guest $$$2$$$ and guest $$$3$$$: $$$\sqrt{3+11} \approx 3.741657387$$$

Guest $$$2$$$ and guest $$$4$$$: $$$\sqrt{3+2} \approx 2.236067977$$$

Guest $$$2$$$ and guest $$$5$$$: $$$\sqrt{3+17} \approx 4.472135955$$$

Guest $$$3$$$ and guest $$$4$$$: $$$\sqrt{11+2} \approx 3.605551275$$$

Guest $$$3$$$ and guest $$$5$$$: $$$\sqrt{11+17} \approx 5.291502622$$$

Guest $$$4$$$ and guest $$$5$$$: $$$\sqrt{2+17} \approx 4.358898944$$$

Adding them all up gives approximately $$$39.009712$$$.