100922: [AtCoder]ABC092 C - Traveling Plan

Problem Statement

There are $N$ sightseeing spots on the $x$-axis, numbered $1, 2, ..., N$. Spot $i$ is at the point with coordinate $A_i$. It costs $|a - b|$ yen (the currency of Japan) to travel from a point with coordinate $a$ to another point with coordinate $b$ along the axis.

You planned a trip along the axis. In this plan, you first depart from the point with coordinate $0$, then visit the $N$ spots in the order they are numbered, and finally return to the point with coordinate $0$.

However, something came up just before the trip, and you no longer have enough time to visit all the $N$ spots, so you decided to choose some $i$ and cancel the visit to Spot $i$. You will visit the remaining spots as planned in the order they are numbered. You will also depart from and return to the point with coordinate $0$ at the beginning and the end, as planned.

For each $i = 1, 2, ..., N$, find the total cost of travel during the trip when the visit to Spot $i$ is canceled.

Constraints

• $2 \leq N \leq 10^5$
• $-5000 \leq A_i \leq 5000$ ($1 \leq i \leq N$)
• All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $...$ $A_N$

Output

Print $N$ lines. In the $i$-th line, print the total cost of travel during the trip when the visit to Spot $i$ is canceled.

Sample Input 1

3
3 5 -1

Sample Output 1

12
8
10

Spot $1$, $2$ and $3$ are at the points with coordinates $3$, $5$ and $-1$, respectively. For each $i$, the course of the trip and the total cost of travel when the visit to Spot $i$ is canceled, are as follows:

• For $i = 1$, the course of the trip is $0 \rightarrow 5 \rightarrow -1 \rightarrow 0$ and the total cost of travel is $5 + 6 + 1 = 12$ yen.
• For $i = 2$, the course of the trip is $0 \rightarrow 3 \rightarrow -1 \rightarrow 0$ and the total cost of travel is $3 + 4 + 1 = 8$ yen.
• For $i = 3$, the course of the trip is $0 \rightarrow 3 \rightarrow 5 \rightarrow 0$ and the total cost of travel is $3 + 2 + 5 = 10$ yen.

Sample Input 2

5
1 1 1 2 0

Sample Output 2

4
4
4
2
4

Sample Input 3

6
-679 -2409 -3258 3095 -3291 -4462

Sample Output 3

21630
21630
19932
8924
21630
19288