Active Infants

AtCoder

IDabc163_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

4
1 3 4 2

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.

Input #2

6
5 5 6 1 1 1

Output #2

Input #3

6
8 6 9 1 2 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Active Infants",
    "description": {
      "content": "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 c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc163_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ children standing in a line from left to right. The activeness of the $i$\\-th child from the left is $A_i$.\nYou can rearrange these children just one time in any order you like.\nWhen a c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments