<p>You are given an integer array <code>rewardValues</code> of length <code>n</code>, representing the values of rewards.</p>

<p>Initially, your total reward <code>x</code> is 0, and all indices are <strong>unmarked</strong>. You are allowed to perform the following operation <strong>any</strong> number of times:</p>

<ul>
	<li>Choose an <strong>unmarked</strong> index <code>i</code> from the range <code>[0, n - 1]</code>.</li>
	<li>If <code>rewardValues[i]</code> is <strong>greater</strong> than your current total reward <code>x</code>, then add <code>rewardValues[i]</code> to <code>x</code> (i.e., <code>x = x + rewardValues[i]</code>), and <strong>mark</strong> the index <code>i</code>.</li>
</ul>

<p>Return an integer denoting the <strong>maximum </strong><em>total reward</em> you can collect by performing the operations optimally.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">rewardValues = [1,1,3,3]</span></p>

<p><strong>Output:</strong> <span class="example-io">4</span></p>

<p><strong>Explanation:</strong></p>

<p>During the operations, we can choose to mark the indices 0 and 2 in order, and the total reward will be 4, which is the maximum.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">rewardValues = [1,6,4,3,2]</span></p>

<p><strong>Output:</strong> <span class="example-io">11</span></p>

<p><strong>Explanation:</strong></p>

<p>Mark the indices 0, 2, and 1 in order. The total reward will then be 11, which is the maximum.</p>
</div>

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

<ul>
	<li><code>1 &lt;= rewardValues.length &lt;= 2000</code></li>
	<li><code>1 &lt;= rewardValues[i] &lt;= 2000</code></li>
</ul>

import math
from typing import *
from pprint import pprint
from functools import cache
import collections
from copy import deepcopy
import heapq
from queue import PriorityQueue

MOD = 10 ** 9 + 7
P = 256


class Solution:
    def maxTotalReward(self, nums: List[int]):

        nums = list(set(nums))
        nums.sort()
        max_sum = 2*max(nums) - 1 
        n = len(nums)
        res = 0

        dp = [[0 for i in range(n + 1)] for i in range(max_sum + 1)]

        max_reward = 1 

        for i in range(n + 1):
            dp[0][i] = 1
        
        for i in range(1,max_sum + 1):
            for j in range(1, n + 1):
                if nums[j - 1] <= i:
                    if i - nums[j-1] < nums[j-1]:
                        dp[i][j] = dp[i][j] | dp[i - nums[j - 1]][j-1]

                dp[i][j] = dp[i][j] | dp[i][j-1]

                if dp[i][j] == 1:
                    res = max(i,res)
        return res
        
80500