Contest Duration: - (local time) (100 minutes) Back to Home
B - Various distances /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 次元空間内の点 (x_1,\ldots,x_N) が与えられます。

• マンハッタン距離： |x_1|+\ldots+|x_N|
• ユークリッド距離： \sqrt{|x_1|^2+\ldots+|x_N|^2}
• チェビシェフ距離： \max(|x_1|,\ldots,|x_N|)

### 制約

• 1 \leq N \leq 10^5
• -10^5 \leq x_i \leq 10^5
• 入力は全て整数

### 入力

N
x_1 \ldots x_N


### 入力例 1

2
2 -1


### 出力例 1

3
2.236067977499790
2


それぞれ次のように計算されます。

• マンハッタン距離： |2|+|-1|=3
• ユークリッド距離： \sqrt{|2|^2+|-1|^2}=2.236067977499789696\ldots
• チェビシェフ距離： \max(|2|,|-1|)=2

### 入力例 2

10
3 -1 -4 1 -5 9 2 -6 5 -3


### 出力例 2

39
14.387494569938159
9


Score : 200 points

### Problem Statement

Given is a point (x_1,\ldots,x_N) in an N-dimensional space.

Find the Manhattan distance, Euclidian distance, and Chebyshev distance between this point and the origin. Here, each of them is defined as follows:

• The Manhattan distance: |x_1|+\ldots+|x_N|
• The Euclidian distance: \sqrt{|x_1|^2+\ldots+|x_N|^2}
• The Chebyshev distance: \max(|x_1|,\ldots,|x_N|)

### Constraints

• 1 \leq N \leq 10^5
• -10^5 \leq x_i \leq 10^5
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
x_1 \ldots x_N


### Output

Print the Manhattan distance, Euclidian distance, and Chebyshev distance between the given point and the origin, each in its own line. Each value in your print will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.

### Sample Input 1

2
2 -1


### Sample Output 1

3
2.236067977499790
2


Each of the distances is computed as follows:

• The Manhattan distance: |2|+|-1|=3
• The Euclidian distance: \sqrt{|2|^2+|-1|^2}=2.236067977499789696\ldots
• The Chebyshev distance: \max(|2|,|-1|)=2

### Sample Input 2

10
3 -1 -4 1 -5 9 2 -6 5 -3


### Sample Output 2

39
14.387494569938159
9