Contest Duration: - (local time) (100 minutes) Back to Home
E - Active Infants /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 人の幼児が左右一列に並んでおり、左から i 番目の幼児の活発度は A_i です。

あなたは一回だけ、幼児たちを好きな順番に並び替えさせることができます。

はじめ左から x 番目に並んでいた幼児が左から y 番目に移動するとき、うれしさが A_x \times |x-y| だけ生じます。

### 制約

• 2 \leq N \leq 2000
• 1 \leq A_i \leq 10^9
• 入力はすべて整数である。

### 入力

N
A_1 A_2 ... A_N


### 入力例 1

4
1 3 4 2


### 出力例 1

20


### 入力例 2

6
5 5 6 1 1 1


### 出力例 2

58


### 入力例 3

6
8 6 9 1 2 1


### 出力例 3

85


Score : 500 points

### Problem Statement

There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.

You can rearrange these children just one time in any order you like.

When a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x \times |x-y| happiness points.

Find the maximum total happiness points the children can earn.

### Constraints

• 2 \leq N \leq 2000
• 1 \leq A_i \leq 10^9
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N


### Output

Print the maximum total happiness points the children can earn.

### Sample Input 1

4
1 3 4 2


### Sample Output 1

20


If we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 \times |1-3|+3 \times |2-4|+4 \times |3-1|+2 \times |4-2|=20 happiness points in total.

### Sample Input 2

6
5 5 6 1 1 1


### Sample Output 2

58


### Sample Input 3

6
8 6 9 1 2 1


### Sample Output 3

85