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: Accepted)

import kotlin.math.abs
import kotlin.math.max

class MaxHappinessCalculator(
    private val n: Int,
    private val a: Array<Long>
) {
    private val memo = Array(n + 1) { Array(n + 1) { null as Long?} }
    private val sorted = (0 until n).sortedByDescending { a[it] }

    private fun calcFromMemo(l: Int, r: Int): Long {
        val memoed = memo[l][r]
        if (memoed != null) {
            return memoed
        }

        val ans = calc(l, r)
        memo[l][r] = ans
        return ans
    }

    fun calc(l: Int, r: Int): Long {
        val m = l + r
        if (m == n) {
            return 0
        }

        val i = sorted[m]
        val lans = calcFromMemo(l + 1, r) + a[i] * abs(l - i)
        val rans = calcFromMemo(l, r + 1) + a[i] * abs((n - r - 1) - i)

        return max(lans, rans)
    }
}

fun main() {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toLong() }.toTypedArray()

    val ans = MaxHappinessCalculator(n, a).calc(0, 0)
    println(ans)
}