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)

#pragma region
#include <bits/stdc++.h>

#define rep(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define reps(i, n) for (int i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i)
#define rreps(i, n) for (int i = ((int)(n)); i > 0; --i)
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define eb emplace_back
#define debug(x) cerr << #x << ": " << x << '\n'
#define INF 1e9
using namespace std;
template <class T = int>
T in() {
  T x;
  cin >> x;
  return (x);
}

typedef long long ll;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

#pragma endregion

int main() {
  int n = in();
  vector<int> a(n);
  auto compare = [](tuple<int, int, int> a, tuple<int, int, int> b) {
    return get<0>(a) < get<0>(b);
  };
  priority_queue<tuple<int, int, int>, vector<tuple<int, int, int> >,
                 decltype(compare)>
      que{compare};
  rep(i, n) {
    a[i] = in();
    rep(j, n) { que.push(make_tuple(a[i] * abs(i - j), i, j)); }
  }
  int count = 0;
  ll ans = 0;
  vector<bool> used(n, false);
  vector<bool> used2(n, false);
  while (!que.empty()) {
    if (!used[get<1>(que.top())] && !used2[get<2>(que.top())]) {
      ans += get<0>(que.top());
      used[get<1>(que.top())] = true;
      used2[get<2>(que.top())] = true;
      que.pop();
    } else {
      que.pop();
    }
  }
  cout << ans << endl;
  return 0;
}