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)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main() {
    int n;
    cin >> n;
    vector<ll> a(n);
    rep(i, n) cin >> a[i];
    bool used[n];
    
    ll res = 0;
    
    ll upper = n;
    ll lower = 1;
    rep(i, n){
        ll max_now = 0;
        ll max_idx = -1;
        rep(j, n){
            if(!used[j]){
                ll dist = max(upper - j - 1, j + 1 - lower);
                if(max_now < dist * a[j]){
                    max_now = dist * a[j];
                    max_idx = j;
                }
            }
        }
        // cout << max_now << endl;
        res += max_now;
        used[max_idx] = true;
        if(upper - max_idx - 1 > max_idx + 1 - lower){
            upper -= 1;
        }else{
            lower += 1;
        }
    }
  
    cout << res << endl;
    return 0;
}