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)

package main

import (
	"fmt"
	"sort"
)

type As [][]int

func (a As) Len() int {
	return len(a)
}

func (a As) Swap(i, j int) {
	a[i], a[j] = a[j], a[i]
}

func (a As) Less(i, j int) bool {
	return a[i][0] > a[j][0]
}

func main() {
	var n int
	fmt.Scan(&n)
	as := make(As, n)
	os := make([]int, n)
	for i := range as {
		var a int
		fmt.Scan(&a)
		as[i] = []int{a, i}
		os[i] = a
	}
	sort.Sort(as)
	var sum int
	l := 0
	r := n - 1
	m := make(map[int]bool)
	for i := range as {
		a, p := as[i][0], as[i][1]
		m[p] = true
		ls := a * abs(p-l)
		for j := l; j < p; j++ {
			if _, ok := m[j]; ok {
				continue
			}
			ls += os[j]
		}
		rs := a * abs(r-p)
		for j := p + 1; j <= r; j++ {
			if _, ok := m[j]; ok {
				continue
			}
			rs += os[j]
		}

		if ls > rs {
			sum += a * abs(p-l)
			//fmt.Println("[l] ls,rs: ", ls, rs)
			l += 1
		} else {
			sum += a * abs(r-p)
			//fmt.Println("[r] ls,rs: ", ls, rs)
			r -= 1
		}
	}
	fmt.Println(sum)
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}