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## 문제

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 the optimal picks.

Find the expected costs of treasures picked by both pirates.

## 입력

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 the optimal picks.

Find the expected costs of treasures picked by both pirates.

## 출력

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

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

## 예제 입력 1

2
1 3


## 예제 출력 1

3.000000000000000 1.000000000000000


## 예제 입력 2

3
2 1 4


## 예제 출력 2

5.500000000000000 1.500000000000000