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 Ruby (2.7.1) (judge verdict: Runtime Error)

use proconio::input;
use std::cmp;

fn dfs(g: &Vec<Vec<usize>>, c: &Vec<usize>, res: &mut Vec<usize>, cnt: &mut Vec<i64>,
       v: usize, p: i64) -> i64 {
  let mut sz: i64 = 1;
  let tmp = cnt[c[v]];

  for &u in &g[v] {
    cnt[c[v]] = 0;
    if u as i64 != p {
      sz += dfs(g, c, res, cnt, u, v as i64);
    }
  }

  cnt[c[v]] = -sz + tmp;

  if p == -1 {
    for (i, &x) in cnt.iter().enumerate() {
      let x = (x + sz) as usize;
      if x != 0 {
        res[i] -= x * (x - 1) / 2 + x;
      }
    }
  } else {
    let x = (cnt[c[p as usize]] + sz) as usize;
    if x != 0 {
      res[c[p as usize]] -= x * (x-1) / 2 + x;
      // println!("{} {}: {} {}", v, c[p as usize], x, res[c[p as usize]]);
    }
  }

  // for (i, &x) in cnt.iter().enumerate() {
    // print!("({}: {}) ", i, x);
  // }
  // println!();

  sz
}

fn main() {
  input! {
    n: usize,
    mut c: [usize; n],
    e: [(usize, usize); n-1],
  }
  let mut g = vec![Vec::<usize>::new(); n];
  for x in &mut c {
    *x -= 1;
  }
  for (a, b) in e {
    g[a-1].push(b-1);
    g[b-1].push(a-1);
  }

  let mut res = vec![n*(n-1)/2 + n; n];
  let mut cnt = vec![0i64; n];

  dfs(&g, &c, &mut res, &mut cnt, 0, -1);

  for x in res {
    println!("{}", x);
  }
}