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)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdint.h> // uint64_t

#define max(a,b) ((a) > (b) ? (a) : (b))
#define min(a,b) ((a) > (b) ? (b) : (a))
#define ARR_MAX 2000
#define BUF_SIZE (ARR_MAX*11+50)

int get_int(void) {
  int num;
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return 0;
  sscanf(line, "%d", &num);
#else
#error
#endif
  return num;
}

// <arr[0]> <arr[1]> .. <arr[size-1]>
int fget_array(int *arr, int size) {
#ifdef BUF_SIZE
    char line[BUF_SIZE];
    char *tmpbuf = line;
    int i;
    if(!fgets(line, BUF_SIZE, stdin)) return -1;
    for(i = 0; i < size; i++) {
        char *tmp = strtok(tmpbuf, " ");
        arr[i] = strtol(tmp, NULL, 10);
        tmpbuf = NULL;
    }
#else
#error
#endif
    return 0;
}

struct pair {
    uint64_t elem;
    int idx;
};

int desc_by_elem(const void *a1, const void *a2) {
    struct pair *pa1 =(struct pair*)a1;
    struct pair *pa2 =(struct pair*)a2;
    int e1 = pa1->elem;
    int e2 = pa2->elem;
    return e2 - e1;
}


int main(void) {
    int num = get_int();
    int arr[ARR_MAX];
    static uint64_t dp[ARR_MAX+1][ARR_MAX+1];
    fget_array(arr, num);
    struct pair brr[ARR_MAX];
    int i, j;
    // brr: 1-indexed
    for(i = 0; i < num; i++) brr[i] = (struct pair){arr[i], i};

    qsort(brr, num, sizeof(struct pair), desc_by_elem);

    for(i = 1; i <= num; i++) {
        struct pair p = brr[i-1];
        for(j = 0; j < i; j++) {
            int head = j;
            int tail = num - (i-j);
#ifdef DEBUG
            printf("%d, %d -> %d %d\n", i, j, head, tail);
#endif
            dp[i][j+1] = max(
                dp[i][j+1],
                dp[i-1][j] + p.elem * abs(p.idx - head)
            );
            dp[i][j] = max(
                dp[i][j],
                dp[i-1][j] + p.elem * abs(tail - p.idx)
            );
        }
    }

    uint64_t ans = 0;
    for(i = 0; i <= num; i++) {
        ans = max(ans, dp[num][i]);
    }
    printf("%llu\n", ans);
    return 0;
}