<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>

class Solution:
    def maxTotalReward(self, rewardValues: List[int]) -> int:
        rewardValues = sorted(set(rewardValues), reverse=True)

        n = len(rewardValues)
        limit = 2*rewardValues[0]+1
        dp = [[0] * (limit+1)for _ in range(n)]

        for l in range(limit+1):
            dp[n-1][l] = 0 if rewardValues[n-1] >= l else rewardValues[n-1]
        for i in range(n-2, -1, -1):
            for l in range(limit+1):
                select = dp[i+1][max(0, min(rewardValues[i], l - rewardValues[i]))] + rewardValues[i]
                not_select = dp[i+1][l]
                select = select if select < l else 0
                dp[i][l] = max(select, not_select)
        # @cache
        # def f(i=0, limit=10000):
        #     if i == len(rewardValues): return 0
        #     if limit <= rewardValues[i]: return f(i+1, limit)
        #     select = f(i+1, max(0, min(rewardValues[i], limit - rewardValues[i]))) + rewardValues[i]
        #     not_select = f(i+1, limit)

        #     # print(rewardValues[i], limit, select, not_select)
            
            
        #     return max(select, not_select)
        # print(dp)
        return dp[0][limit]
251300