Chat in a Circle

AtCoder

IDabc173_d

Time2000ms

Memory256MB

Difficulty—

Quickly after finishing the tutorial of the online game _ATChat_, you have decided to visit a particular place with $N-1$ players who happen to be there. These $N$ players, including you, are numbered $1$ through $N$, and the **friendliness** of Player $i$ is $A_i$. The $N$ players will arrive at the place one by one in some order. To make sure nobody gets lost, you have set the following rule: players who have already arrived there should form a circle, and a player who has just arrived there should cut into the circle somewhere. When each player, except the first one to arrive, arrives at the place, the player gets **comfort** equal to the smaller of the friendliness of the clockwise adjacent player and that of the counter-clockwise adjacent player. The first player to arrive there gets the comfort of $0$. What is the maximum total comfort the $N$ players can get by optimally choosing the order of arrivals and the positions in the circle to cut into? ## Constraints * All values in input are integers. * $2 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

4
2 2 1 3

Output #1

7

By arriving at the place in the order Player $4, 2, 1, 3$, and cutting into the circle as shown in the figure, they can get the total comfort of $7$.
![image](https://img.atcoder.jp/ghi/766a260a0019ea93e86e0588cc4db868.png)
They cannot get the total comfort greater than $7$, so the answer is $7$.

Input #2

7
1 1 1 1 1 1 1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Chat in a Circle",
    "description": {
      "content": "Quickly after finishing the tutorial of the online game _ATChat_, you have decided to visit a particular place with $N-1$ players who happen to be there. These $N$ players, including you, are numbered",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc173_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Quickly after finishing the tutorial of the online game _ATChat_, you have decided to visit a particular place with $N-1$ players who happen to be there. These $N$ players, including you, are numbered...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments