<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 maxSatisfaction(self, satisfaction: List[int]) -> int:
        
        def solve(satisfaction,i,time):
            if i==len(satisfaction):
                return 0
            inclu=(time+1)*satisfaction[i]+solve(satisfaction,i+1,time+1)
            exclu=solve(satisfaction,i+1,time)
            return max(inclu,exclu)    

        def solveMemo(satisfaction,i,time,dp):
            if i==len(satisfaction):
                return 0
            if dp[i][time]!=-1:
                return dp[i][time]         
            inclu=(time+1)*satisfaction[i]+solveMemo(satisfaction,i+1,time+1,dp)
            exclu=solveMemo(satisfaction,i+1,time,dp)
            dp[i][time]=max(inclu,exclu)
            return dp[i][time]   

        def solveTab(satisfaction):
            n=len(satisfaction)
            dp=[[0]*(n+1) for i in range(n+1)]         
            for i in range(n-1,-1,-1):
                for time in range(n-1,-1,-1):
                    inclu=(time+1)*satisfaction[i]+dp[i+1][time+1]
                    exclu=dp[i+1][time]
                    dp[i][time]=max(inclu,exclu)
            return dp[0][0]

        def help(satisfaction):    
            satisfaction.sort()    
            # return solve(satisfaction,0,0)

            dp=[[-1]*(len(satisfaction)+1) for i in range(len(satisfaction)+1)]
            # return solveMemo(satisfaction,0,0,dp)    

            return solveTab(satisfaction)
        return help(satisfaction)    

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