Problem:
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

Solution in Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var (
	N int
	A []int
)

func main() {
	defer writer.Flush()
	readVariables()
	sort.Slice(A, func(i, j int) bool {
		return A[i] > A[j]
	})
	q := NewIntPriorityQueue(func(x, y int) bool {
		return x > y
	})
	heap.Push(q, A[0])
	var answer int
	for i := 1; i < N; i++ {
		v := heap.Pop(q).(int)
		answer += v
		next := MinInt(v, A[i])
		heap.Push(q, next)
		heap.Push(q, next) // 2回追加する
	}
	println(answer)
}

func readVariables() {
	N = nextInt()
	A = make([]int, N)
	for i := 0; i < N; i++ {
		A[i] = nextInt()
	}

}

/* Template */

var (
	scanner *bufio.Scanner
	writer  *bufio.Writer
)

func init() {
	Max := 1001001
	scanner = bufio.NewScanner(os.Stdin)
	scanner.Buffer(make([]byte, 0, Max), Max)
	scanner.Split(bufio.ScanWords)
	writer = bufio.NewWriterSize(os.Stdout, Max)
}

func println(a ...interface{}) {
	fmt.Fprintln(writer, a...)
}

func printf(format string, a ...interface{}) {
	fmt.Fprintf(writer, format, a...)
}

//nextInt converts next token from stdin and returns integer value.
//nextInt panics when conversion into an integer fails.
func nextInt() int {
	if !scanner.Scan() {
		panic("No more token.")
	}
	num, err := strconv.Atoi(scanner.Text())
	if err != nil {
		panic("nextInt(): cannot convert to int: " + scanner.Text())
	}
	return num
}

func nextStr() string {
	if !scanner.Scan() {
		panic("No more token.")
	}
	return scanner.Text()
}

// MinInt returns minimum argument
func MinInt(x, y int) int {
	if x < y {
		return x
	} else {
		return y
	}
}

//MaxInt returns maximum argument
func MaxInt(x, y int) int {
	if x < y {
		return y
	} else {
		return x
	}
}

//AbsInt returns |x| for x
func AbsInt(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

// IntPriorityQueue は、整数値の優先度付きキューを表す。
type IntPriorityQueue struct {
	values  []int
	lessVal func(x, y int) bool // indexではなく値を比較するless関数
}

// NewIntPriorityQueue は、引数のless関数で整数値を比較するIntPriorityQueueを生成する。
func NewIntPriorityQueue(lessVal func(x, y int) bool) *IntPriorityQueue {
	q := &IntPriorityQueue{
		values:  make([]int, 0),
		lessVal: lessVal,
	}
	heap.Init(q)
	return q
}

// Len は、要素数を返す。
func (q *IntPriorityQueue) Len() int {
	return len(q.values)
}

// Less は、比較関数
func (q *IntPriorityQueue) Less(i, j int) bool {
	return q.lessVal(q.values[i], q.values[j])
}

// Swap は、要素をスワップする
func (q *IntPriorityQueue) Swap(i, j int) {
	q.values[i], q.values[j] = q.values[j], q.values[i]
}

// Pop pops elem
func (q *IntPriorityQueue) Pop() interface{} {
	v := q.values[q.Len()-1]
	q.values = q.values[0 : q.Len()-1]
	return v
}

func (q *IntPriorityQueue) Push(x interface{}) {
	v := x.(int)
	q.values = append(q.values, v)
}