<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;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= rewardValues[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

from bisect import bisect_right

class Solution:
    def maxTotalReward(self, rewardValues: List[int]) -> int:
        if len(rewardValues) == 0:
            return 0
        rewardValues = sorted(set(rewardValues))
        # The last reward must be the max(reward)
        # Therefore, theoretical max total reward is max(reward) * 2 - 1
        return self.getMaxRewardUnderAmount(rewardValues, rewardValues[-1] - 1) + rewardValues[-1]

    def getMaxRewardUnderAmount(self, rewardValues: List[int], maxReward: int):
        startIndex = bisect_right(rewardValues, maxReward) - 1
        if startIndex == -1:
            return 0
        if rewardValues[startIndex] == maxReward:
            return maxReward
        endIndex = bisect_right(rewardValues, (maxReward + 1) >> 1) - 1
        if endIndex == -1:
            endIndex = startIndex
        index = startIndex
        currMax = 0
        while index >= endIndex:
            curr = self.getMaxRewardUnderAmount(rewardValues, min(rewardValues[index] - 1, maxReward - rewardValues[index])) + rewardValues[index]
            if curr == maxReward:
                return maxReward
            elif curr > currMax:
                currMax = curr
            index -= 1
        return currMax
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