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 <iostream>
#include <iomanip>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <algorithm>
#include <cstdio>
#include <utility>
#include <string>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <numeric>

using namespace std;

typedef uint64_t u64;
typedef int64_t s64;
typedef uint32_t u32;
typedef int32_t s32;
typedef vector<s32> vs32;
typedef vector<u32> vu32;
typedef vector<s64> vs64;
typedef vector<u64> vu64;

const double PI=3.14159265358979323846;

#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define MIN(x, y) ((x) > (y) ? (y) : (x))

#define rep(i, N) for(int i = 0; i < N; ++i)

#define CEIL(x, y) (((x) + (y) - 1) / (y))
#define MOD 1000000007ULL

#define IN(l, r, x) ((l) <= (x) && (x) < (r))

using P = pair<int, int>;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    s64 n;
    cin >> n;
    vs64 a(n);
    rep (i, n)
    {
        cin >> a[i];
    }

    priority_queue< pair<s64, pair<s64, P> > > pq;
    rep (i, n)
    {
        rep (j, n)
        {
            pq.push(make_pair(a[i] * abs(i - j), make_pair(-a[i], P{i, j})));
        }
    }

    s64 ans = 0;
    vector< bool > from(n, false);
    vector< bool > to(n, false);
    while (!pq.empty())
    {
        auto p = pq.top(); pq.pop();
        s64 cost = p.first;
        int x = p.second.second.first;
        int y = p.second.second.second;
        if (!from[x] && !to[y])
        {
            ans += cost;
            from[x] = true;
            to[y] = true;
        }
    }

    cout << ans << "\n";
    return 0;
}