<p>You are the manager of a basketball team. For the upcoming tournament, you want to choose the team with the highest overall score. The score of the team is the <strong>sum</strong> of scores of all the players in the team.</p>

<p>However, the basketball team is not allowed to have <strong>conflicts</strong>. A <strong>conflict</strong> exists if a younger player has a <strong>strictly higher</strong> score than an older player. A conflict does <strong>not</strong> occur between players of the same age.</p>

<p>Given two lists, <code>scores</code> and <code>ages</code>, where each <code>scores[i]</code> and <code>ages[i]</code> represents the score and age of the <code>i<sup>th</sup></code> player, respectively, return <em>the highest overall score of all possible basketball teams</em>.</p>

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

<pre>
<strong>Input:</strong> scores = [1,3,5,10,15], ages = [1,2,3,4,5]
<strong>Output:</strong> 34
<strong>Explanation:</strong>&nbsp;You can choose all the players.
</pre>

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

<pre>
<strong>Input:</strong> scores = [4,5,6,5], ages = [2,1,2,1]
<strong>Output:</strong> 16
<strong>Explanation:</strong>&nbsp;It is best to choose the last 3 players. Notice that you are allowed to choose multiple people of the same age.
</pre>

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

<pre>
<strong>Input:</strong> scores = [1,2,3,5], ages = [8,9,10,1]
<strong>Output:</strong> 6
<strong>Explanation:</strong>&nbsp;It is best to choose the first 3 players. 
</pre>

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

<ul>
	<li><code>1 &lt;= scores.length, ages.length &lt;= 1000</code></li>
	<li><code>scores.length == ages.length</code></li>
	<li><code>1 &lt;= scores[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= ages[i] &lt;= 1000</code></li>
</ul>

from functools import cache
class Solution:
    def bestTeamScore(self, scores: List[int], ages: List[int]) -> int:
        
        n = len(ages)
        age_score = [[ages[i],scores[i]] for i in range(n)]
        age_score.sort(key = lambda x:(x[0],x[1]))

        dp = [[-float('inf')]*(n+1) for _ in range(n+1)]
        for j in range(n+1):
            dp[n][j] = 0

        for i in range(n-1,-1,-1):
            for prev in range(i,-1,-1):
                notPick = dp[i+1][prev]
                pick = -float('inf')
                if prev == 0 or age_score[prev-1][0] == age_score[i][0] or age_score[i][1] >= age_score[prev-1][1]:
                    pick = age_score[i][1] + dp[i+1][i+1]
                dp[i][prev] = max(pick,notPick)
                
        return dp[0][0]

        

        
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