1402 - Reducing Dishes.

Hard

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