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.