<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 heapq
class Solution:
    def bestTeamScore(self, scores: List[int], ages: List[int]) -> int:
        pairs=[[scores[i],ages[i]] for i in range(len(scores))]
        pairs.sort() # will sort based on the first element by default
        cache={}
        
        def solve(index,max_age):
            
            if index >= len(scores):
                return 0
            
        
            if (index,max_age) not in cache:
                pick = 0
                
                score,age=pairs[index]

                if age >= max_age: # can pick the player
                    pick = solve(index+1,age) + score
                    

                cache[(index,max_age)] = max(pick ,solve(index+1,max_age))
               
                
            
            return cache[(index,max_age)]

        return solve(0,0)
        
199100