Problem:
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

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

// @problemURL url.com
package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func nt(s *bufio.Scanner) string {
	s.Scan()
	return s.Text()
}

func ni(s *bufio.Scanner) int {
	return atoi(nt(s))
}

func atoi(s string) int {
	i, err := strconv.Atoi(s)
	if err != nil {
		panic(err)
	}
	return i
}

type pair struct {
	x, y, z int
}

func main() {
	var in = bufio.NewReader(os.Stdin)
	s := bufio.NewScanner(in)
	s.Split(bufio.ScanWords)

	// Code
	n := ni(s)
	ar := make([]pair, n)
	for i := 0; i < n; i++ {
		ar[i] = pair{i + 1, ni(s), 0}
	}
	sort.Slice(ar, func(i, j int) bool {
		return ar[i].y < ar[j].y
	})

	i1, i2 := 0, n-1
	var sum int
	for i := n - 1; i >= 0; i-- {
		if abs(ar[i].x-i1) > abs(ar[i].x-i2) {
			ar[i].z = i1 + 1
			i1++
		} else {
			ar[i].z = i2 + 1
			i2--
		}

		sum += ar[i].y * abs(ar[i].x-ar[i].z)
	}

	fmt.Println(sum)
	// fmt.Println(ar)
}

func abs(i int) int {
	if i >= 0 {
		return i
	}
	return -i
}