Problem Statement

In JOI City, there are $N$ residents numbered from $1$ to $N$, and the age of resident $i$ ($1 \le i \le N$) is $A_i$ years old.

The ages $A_1, A_2, \dots, A_N$ of the residents of JOI City are given. Write a program to find, for each $i = 1, 2, \dots, N$, the maximum age difference between resident $i$ and the other residents.

Constraints

• $2 \le N \le 250000$.
• $0 \le A_i \le 10^9$ ($1 \le i \le N$).
• All input values are integers.

Subtasks

1. ($25$ points) $N = 2$.
2. ($30$ points) $N \le 1000$.
3. ($45$ points) No additional constraints.

Input

The input is given in the following format:

$N$ $A_1 \ A_2 \ \dots \ A_N$

Output

Output $N$ lines. On the $i$-th line ($1 \le i \le N$), output the maximum age difference between resident $i$ and the other residents.

Sample Input and Output

Sample Input 1

3
13 15 20

Sample Output 1

7
5
7

• The age differences between resident $1$ and residents $2, 3$ are $2, 7$ years, respectively. Since their maximum value is $7$ years, output $7$ on the $1$-st line.
• The age differences between resident $2$ and residents $1, 3$ are $2, 5$ years, respectively. Since their maximum value is $5$ years, output $5$ on the $2$-nd line.
• The age differences between resident $3$ and residents $1, 2$ are $7, 5$ years, respectively. Since their maximum value is $7$ years, output $7$ on the $3$-rd line.

This sample input satisfies the constraints of Subtasks $2, 3$.

Sample Input 2

2
100 100

Sample Output 2

0
0

• The age difference between resident $1$ and resident $2$ is $0$ years. Therefore, output $0$ on the $1$-st line.
• The age difference between resident $2$ and resident $1$ is $0$ years. Therefore, output $0$ on the $2$-nd line.

This sample input satisfies the constraints of all subtasks.

Sample Input 3

10
440894064 101089692 556439322 34369336 98417847 216265879 623843484 554560874 247445405 718003331

Sample Output 3

406524728
616913639
522069986
683633995
619585484
501737452
589474148
520191538
470557926
683633995

This sample input satisfies the constraints of Subtasks $2, 3$.