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: Accepted)

/*Bismillahir Rahmanir Rahim*///{
#include <bits/stdc++.h>
#include <ext/numeric>
using namespace std; using __gnu_cxx::power;
using ll = long long; using ull = unsigned long long; using ld = long double;
const ll llinf = (1ll<<61)-1;
const double eps = 1e-6, ldeps = 1e-9;
struct Dbg {
static constexpr auto &os = cout;   // replace by cerr in interactive.
template<class C> static auto dud(C *x)->decltype(os << *x, 0);
template<class C> static char dud(...);
template<class C> typename enable_if<sizeof dud<C>(0)!=1, Dbg&>::type operator<<(const C &x) { os << x; return *this; }
template<class C> Dbg &dump(C b, C e) {
    *this << "\n[";
    int cur = 0;
    for (C i = b; i!=e and cur<26; i++, cur++) *this << ", "+2*(i==b) << *i;
    return *this << ']';
}
template<class C> typename enable_if<sizeof dud<C>(0)==1, Dbg&>::type operator<<(const C &x) {
    return dump(begin(x), end(x));
}
template<class C, size_t X> typename enable_if<!is_same<C, const char>::value, Dbg&>::type operator <<(C (&x)[X]) {
    return dump(begin(x), end(x));
}
template<class B, class C> Dbg &operator <<(const pair<B, C> &x) {
    return *this << '{' << x.first << ", " << x.second << '}';
}
Dbg &operator<<(ostream&(*x)(std::ostream&)) { os << x; return *this; }
} dbg;
void err(istringstream *iss) { delete iss; }
template<class C, class... Args> void err(istringstream *iss, const C &val, const Args &... args) {
    string name; *iss >> name; if (name.back()==',') name.pop_back();
    dbg << name << " = " << val << "; ", err(iss, args...);
}
#define bug(args...) dbg << __LINE__ << ": ", err(new istringstream(#args), args), dbg << endl
#define cbug(a, args...) if (a) bug(args);
#define ASSERT(a, o, b, args...) if (!((a)o(b))) bug(a, b, ##args), assert((a)o(b));
#define sl(a) int(strlen(a))
#define sz(a) int(a.size())
int T, Q, cn;//}
const int inf = 1000000007, mxn = 2005;

int n;
pair<int, int> a[mxn];
ll memo[mxn][mxn];
bitset<mxn> vstd[mxn];
ll dp(int at, int l) {
    if (at == n+1) return 0;
    auto &ret = memo[at][l];
    if (vstd[at][l]) return ret;
    vstd[at][l] = 1;
    int r = n-(at-l);
    ret = max(abs(a[at].second-l)*ll(a[at].first)+dp(at+1, l+1), abs(a[at].second-r)*ll(a[at].first)+dp(at+1, l));
    return ret;
}

signed main() { cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit); cout.precision(11);
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> a[i].first, a[i].second = i;
    }
    sort(a+1, a+1+n, greater<pair<int, int>> ());
    cout << dp(1, 1) << '\n';
}