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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.io.PrintWriter
import kotlin.math.abs
import java.util.ArrayDeque

fun main() {
    val pw = PrintWriter(System.out)

    val n = readInputLine().toInt()
    val aArr = readInputLine().split(" ").map { it.toLong() }.toLongArray()
    val ansArr = IntArray(n) { -1 }

    val queue = ArrayDeque<Int>()

    repeat(n) {
        queue.add(it)
    }

    while (queue.isNotEmpty()) {
        val p = queue.poll()!!
        for (i in n downTo 0) {
            if (p - i > 0) {
                if (ansArr[p - i] == -1) {
                    ansArr[p - i] = p
                    break
                } else {
                    val reserved = ansArr[p - i]
                    if (abs(reserved - (p - i)) * aArr[reserved] < abs(p - (p - i)) * aArr[p]) {
                        ansArr[p - i] = p
                        queue.add(reserved)
                        break
                    }
                }
            }
            if (p + i < n) {
                if (ansArr[p + i] == -1) {
                    ansArr[p + i] = p
                    break
                } else {
                    val reserved = ansArr[p + i]
                    if (abs(reserved - (p + i)) * aArr[reserved] < abs(p - (p + i)) * aArr[p]) {
                        ansArr[p + i] = p
                        queue.add(reserved)
                        break
                    }
                }
            }
        }
    }

    var ans = 0L

    repeat(n) {
        ans += abs(ansArr[it] - it) * aArr[it]
    }

    pw.println(ans)

    pw.flush()
}

fun readInputLine(): String {
    return readLine()!!
}