<p>A chef has collected data on the <code>satisfaction</code> level of his <code>n</code> dishes. Chef can cook any dish in 1 unit of time.</p>

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

<p>Return the maximum sum of <strong>like-time coefficient </strong>that the chef can obtain after preparing some amount of dishes.</p>

<p>Dishes can be prepared in <strong>any </strong>order and the chef can discard some dishes to get this maximum value.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

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

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == satisfaction.length</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>-1000 &lt;= satisfaction[i] &lt;= 1000</code></li>
</ul>

class Solution:
    def solution(self, s, index, time, dp):
        if index == len(s):
            return 0

        if dp[index][time] != -1:
            return dp[index][time]

        include = s[index] * (time+1) + self.solution(s, index+1, time+1, dp)
        exclude = self.solution(s, index+1, time, dp)
        dp[index][time] = max(include, exclude)
        return dp[index][time]

    def maxSatisfaction(self, satisfaction: List[int]) -> int:
        satisfaction.sort()
        n = len(satisfaction)
        dp = [[0]*(n+1) for _ in range(n+1)]
        # answer = self.solution(satisfaction, 0, 0, dp)

        for i in reversed(range(n)):
            for j in reversed(range(i+1)): # max time to prepare i dishes is i.
                include = satisfaction[i] * (j+1) + dp[i+1][j+1]
                exclude = dp[i+1][j]
                dp[i][j] = max(include, exclude)
        return dp[0][0]
22600