<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>

import numpy as np
class Solution:
    def bestTeamScore(self, scores: List[int], ages: List[int]) -> int:
        n = len(scores)
        ind = np.lexsort((scores, ages)) #within the same ages, sort according to scores
        scores = np.array(scores)
        ages = np.array(ages)
        scores = scores[ind]
        ages = ages[ind]

        dp = [scores[i] for i in range(n)]
        for i in range(1,n):
            for j in range(i-1, -1, -1):
                if ages[j] < ages[i] and scores[j] > scores[i]:
                    continue
                else:
                    dp[i] = max(dp[i], scores[i] + dp[j])

        return max(dp)

        # @cache
        # def rec(i):
        #     #return the best team with ages smaller than ages[i]
        #     if i == 0:
        #         return scores[i]
        #     else:
        #         tmp = scores[i]
        #         for j in range(i-1, -1, -1):
        #             if ages[j] < ages[i] and scores[j] > scores[i]:
        #                 continue
        #             else:
        #                 tmp = max(tmp, scores[i] + rec(j))

        #         return tmp
        
        # return max([rec(i) for i in range(n)])


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