A chef has collected data on the `satisfaction` level of his `n` dishes. Chef can cook any dish in 1 unit of time.

Like-time coefficient of a dish is defined as the time taken to cook that dish including previous dishes multiplied by its satisfaction level i.e. `time[i] * satisfaction[i]`.

Return the maximum sum of like-time coefficient that the chef can obtain after dishes preparation.

Dishes can be prepared in any order and the chef can discard some dishes to get this maximum value.

Example 1:

    Input: satisfaction = [-1,-8,0,5,-9]
    Output: 14
    Explanation: After Removing the second and last dish, the maximum total like-time coefficient will be equal to (-1*1 + 0*2 + 5*3 = 14).
    Each dish is prepared in one unit of time.

Example 2:

    Input: satisfaction = [4,3,2]
    Output: 20
    Explanation: Dishes can be prepared in any order, (2*1 + 3*2 + 4*3 = 20)

Example 3:

    Input: satisfaction = [-1,-4,-5]
    Output: 0
    Explanation: People do not like the dishes. No dish is prepared.

Constraints:

- `n == satisfaction.length`
- `1 <= n <= 500`
- `-1000 <= satisfaction[i] <= 1000`