407880: GYM102916 D Two Pirates - 2

Two pirates are dividing looted treasures. There are $$$n$$$ treasures, the $$$i$$$-th of which costs $$$a_i$$$ gold. They move in rotation, each turn a pirate picks one of the remaining treasures. The thing is, the second pirate is drunk, so he doesn't make optimal picks and each turn just picks a random available treasure, uniformly. The first pirate knows that and always makes optimal picks.

Find the expected costs of treasures picked by both pirates.

The first line contains an integer $$$n$$$ ($$$1 \le n \le 5000$$$) — the number of treasures.

The second line contains $$$n$$$ integers $$$a_i$$$ ($$$1 \le a_i \le 10^9$$$) — the costs of the treasures.

Output two floating-point numbers: the expected costs of treasures picked by the first and the second pirates.

The absolute or relative error of the numbers shouldn't exceed $$$10^{-9}$$$.

2
1 3

3.000000000000000 1.000000000000000

3
2 1 4

5.500000000000000 1.500000000000000