"""
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

analysis:
TC: O(N log N)
SC: O(1)
"""
from typing import List


class Solution:
    def maxSatisfaction(self, satisfaction: List[int]) -> int:
        n = len(satisfaction)
        satisfaction.sort()
        res = suff_sum = 0
        i = n - 1
        while i >= 0 and suff_sum + satisfaction[i] > 0:
            suff_sum += satisfaction[i]
            res += suff_sum
            i -= 1
        return res