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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

// インクルード
#include <bits/stdc++.h>

// 名前空間省略
using namespace std;

// メイン関数
int main()
{
	// 標準入出力　高速化
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	int n;
	cin >> n;
	int *a = new int[n+1];
	// int *b = new int[n+1];
	vector<bool> c(n+1,false);

	for(int i=1;i<=n;i++){
		// b[i]=i;
		cin >> a[i];
	}

	int min=1;
	int max=n;
	long long sum=0;

	for(int i=1;i<=n;i++){
		int k=0;
		bool flag=false;
		long long c_max=0;

		for(int j=1;j<=n;j++){
			if(c[j]==true) continue;

			if(abs(j-min) < abs(j-max)){
				if(c_max < (long long)a[j] * abs(j-max)){
					c_max = (long long)a[j] * abs(j-max);
					flag = true;
					k=j;
				}
			}
			else{
				if(c_max < (long long)a[j] * abs(j-min)){
					c_max = (long long)a[j] * abs(j-min);
					flag =false;
					k=j;
				}
			}
		}

		sum += c_max;
		if(flag == true) max--;
		if(flag == false) min++;
		c[k] = true;

	}

	cout << sum << endl;
}