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>
using namespace std;
#define F(i,a,b) for(int i=a;i<b;i++)
#define f(i,n) for(int i=0;i<n;i++)
typedef unsigned long long ull;
typedef long long ll;
#define vint vector<int>
#define pb(a) push_back(a);
#define bug(x) cout<<#x<<" = "<<x<<endl;
#define fastio ios_base::sync_with_stdio(false); cin.tie(0);

const int M=1000000007;

ull pow(ull a,ull p){
    if(p==1){return a%M;}
    if(p%2==0){
        ull temp=pow(a,p/2);
        return (temp*temp)%M;
    }
    return ((pow(a,p-1)%M)*a)%M;
    
}

int main(){
	// fastio;
	int n;
    cin>>n;
    int a[n],b[n],c[n];
    int l=0,r=n-1;
    int index=0;
    f(i,n){
        cin>>a[i];
        b[i]=a[i];
    }
    sort(b,b+n,greater<int>());
    int ans=0;
    // f(i,n){
    //     cout<<b[i]<<" ";
    // }cout<<endl;
    f(i,n){
        f(j,n){
            if(a[j]==b[i]){
                index = j;
            }
        }
        int temp=a[index];
        a[index]=-1;
        // cout<<"("<<a[index]<<") --> ";
        if(abs(index-l) > abs(r-index) ){
            ans+=(abs(index-l)*temp);
            c[l]=temp;
            l++;
        }
        else{
            ans+=(abs(r-index)*temp);
            c[r]=temp;
            r--;
        }
        // if(l>r){
        //     break;
        // }
        // cout<<ans<<endl;
        // bug(l); bug(r);
    }

    // f(i,n){
    //     cout<<c[i]<<" ";
    // }
    // cout<<endl;
    cout<<ans<<"\n";
    return 0;
}