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)

// Beginner163.cpp : This file contains the 'main' function. Program execution begins and ends there.
//
#define _USE_MATH_DEFINES

#include <bits/stdc++.h>
#include <math.h>

using namespace std;

typedef long long ll;
typedef tuple<int,int,int> pp;




struct CustomCompare
{
	bool operator()(const pp& lhs, const pp& rhs)
	{
		return std::get<2>(lhs) < std::get<2>(rhs);
	}
};


int main()
{
	//A
    /*double r;
	cin >> r;
	cout << 2 * M_PI * r;*/

	//B
	/*int n, m;
	cin >> n >> m;
	int res = n;
	int a;
	for (int i = 0; i < m; ++i)
	{
		cin >> a;
		res -= a;
	}
	cout << (res >= 0 ? res : -1);*/

	//C
	/*int n;
	cin >> n;
	vector<int>a(n);
	a[0] = 0;
	map<int, int> res;
	for (int i = 1; i < n; ++i)
	{
		cin >> a[i];
		a[i]--;
		res[a[i]]++;
	}

	for (int i = 0; i < n; ++i)
	{
		cout << res[i] << '\n';
	}*/

	//D
	/*ll n, k;
	cin >> n >> k;
	const ll modValue = 1e9 + 7;
	
	ll res = 0;
	for (ll i = k; i <= n + 1; ++i)
	{
		ll min = (0 + i-1) * i / 2;
		ll max = (n - (i-1) + n) * i / 2;
		res += max - min + 1;
		res %= modValue;
	}

	cout << res;*/

	//E
	int n;
	cin >> n;
	vector<int> a(n);
	priority_queue<pp, vector<pp>, CustomCompare> q;
	map<int, int> positions;
	vector<bool> occupied(n, false);
	vector<bool> used(n, false);

	
	for (int i = 0; i < n; ++i)
	{
		cin >> a[i];
		positions[a[i]] = i;
		for (int j = 0; j < n; ++j)
		{
			auto t = make_tuple(i, j, a[i] * abs(i - j));
			q.push(t);
		}
	}
	
	ll result = 0;
	while (find(used.begin(), used.end(), false) != used.end())
	{
		auto top = q.top();
		q.pop();
		int from = std::get<0>(top);
		int to = std::get<1>(top);
		int sum = std::get<2>(top);
		if (used[from]) continue;
		if (occupied[to]) continue;
		result += sum;
		used[from] = true;
		occupied[to] = true;
		
	}

	cout << result;
}