<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>

class Solution:
    def bestTeamScore(self, scores: List[int], ages: List[int]) -> int:
        scoreIndex = [i for i in range(len(scores))]
        scoreIndex.sort(key=lambda x: (ages[x], scores[x]))
        scores = [scores[i] for i in scoreIndex]
        ages = [ages[i] for i in scoreIndex]
        self.scores, self.ages = scores, ages
        self.result = 0
        self.dp = {}
        return self.recurse(len(scores) - 1, -1)

    def recurse(self, index: int, maxIndex: int) -> int:
        if index == -1:
            return 0
        key = (index, maxIndex)
        if key in self.dp:
            return self.dp[key]
        score, age = self.scores[index], self.ages[index]
        curScore = self.recurse(index - 1, maxIndex)
        if maxIndex == -1 or score <= self.scores[maxIndex] or age == self.ages[maxIndex]:
            if maxIndex == -1 or score < self.scores[maxIndex]:
                curScore = max(curScore, score + self.recurse(index - 1, index))
            else:
                curScore = max(curScore, score + self.recurse(index - 1, maxIndex))
        self.dp[key] = curScore
        return curScore
98400