Contest Duration: - (local time) (100 minutes) Back to Home
D - Chat in a Circle /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

あなたはオンラインゲーム「ATChat」のチュートリアルを終え、その場に居合わせたプレイヤー N 人で早速とある場所を訪ねることにしました。この N 人には 1 から N の番号が振られており、人 i\ (1 \leq i \leq N)フレンドリーさA_i です。

N 人が到着する順番や割り込む位置を適切に決めたとき、N 人の心地よさの合計の最大値はいくらになるでしょう？

### 制約

• 入力はすべて整数
• 2 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq 10^9

### 入力

N
A_1 A_2 \dots A_N


### 出力

N 人の心地よさの合計の最大値を出力せよ。

### 入力例 1

4
2 2 1 3


### 出力例 1

7


4, 2, 1, 3 がこの順に到着し、図のように輪に割り込むことで、心地よさの合計は 7 になります。

### 入力例 2

7
1 1 1 1 1 1 1


### 出力例 2

6


Score: 400 points

### Problem Statement

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


### Output

Print the maximum total comfort the N players can get.

### Sample Input 1

4
2 2 1 3


### Sample 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.

They cannot get the total comfort greater than 7, so the answer is 7.

### Sample Input 2

7
1 1 1 1 1 1 1


### Sample Output 2

6