<p>Alice is a caretaker of <code>n</code> gardens and she wants to plant flowers to maximize the total beauty of all her gardens.</p>

<p>You are given a <strong>0-indexed</strong> integer array <code>flowers</code> of size <code>n</code>, where <code>flowers[i]</code> is the number of flowers already planted in the <code>i<sup>th</sup></code> garden. Flowers that are already planted <strong>cannot</strong> be removed. You are then given another integer <code>newFlowers</code>, which is the <strong>maximum</strong> number of flowers that Alice can additionally plant. You are also given the integers <code>target</code>, <code>full</code>, and <code>partial</code>.</p>

<p>A garden is considered <strong>complete</strong> if it has <strong>at least</strong> <code>target</code> flowers. The <strong>total beauty</strong> of the gardens is then determined as the <strong>sum</strong> of the following:</p>

<ul>
	<li>The number of <strong>complete</strong> gardens multiplied by <code>full</code>.</li>
	<li>The <strong>minimum</strong> number of flowers in any of the <strong>incomplete</strong> gardens multiplied by <code>partial</code>. If there are no incomplete gardens, then this value will be <code>0</code>.</li>
</ul>

<p>Return <em>the <strong>maximum</strong> total beauty that Alice can obtain after planting at most </em><code>newFlowers</code><em> flowers.</em></p>

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

<pre>
<strong>Input:</strong> flowers = [1,3,1,1], newFlowers = 7, target = 6, full = 12, partial = 1
<strong>Output:</strong> 14
<strong>Explanation:</strong> Alice can plant
- 2 flowers in the 0<sup>th</sup> garden
- 3 flowers in the 1<sup>st</sup> garden
- 1 flower in the 2<sup>nd</sup> garden
- 1 flower in the 3<sup>rd</sup> garden
The gardens will then be [3,6,2,2]. She planted a total of 2 + 3 + 1 + 1 = 7 flowers.
There is 1 garden that is complete.
The minimum number of flowers in the incomplete gardens is 2.
Thus, the total beauty is 1 * 12 + 2 * 1 = 12 + 2 = 14.
No other way of planting flowers can obtain a total beauty higher than 14.
</pre>

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

<pre>
<strong>Input:</strong> flowers = [2,4,5,3], newFlowers = 10, target = 5, full = 2, partial = 6
<strong>Output:</strong> 30
<strong>Explanation:</strong> Alice can plant
- 3 flowers in the 0<sup>th</sup> garden
- 0 flowers in the 1<sup>st</sup> garden
- 0 flowers in the 2<sup>nd</sup> garden
- 2 flowers in the 3<sup>rd</sup> garden
The gardens will then be [5,4,5,5]. She planted a total of 3 + 0 + 0 + 2 = 5 flowers.
There are 3 gardens that are complete.
The minimum number of flowers in the incomplete gardens is 4.
Thus, the total beauty is 3 * 2 + 4 * 6 = 6 + 24 = 30.
No other way of planting flowers can obtain a total beauty higher than 30.
Note that Alice could make all the gardens complete but in this case, she would obtain a lower total beauty.
</pre>

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

<ul>
	<li><code>1 &lt;= flowers.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= flowers[i], target &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= newFlowers &lt;= 10<sup>10</sup></code></li>
	<li><code>1 &lt;= full, partial &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def maximumBeauty(self, flowers: List[int], newFlowers: int, target: int, full: int, partial: int) -> int:
        flowers.sort()
        end = bisect.bisect_left(flowers,target)
        initial = full*(len(flowers)-end)
        if end==0:
            return initial
        ans = 0
        j = end-1
        used = 0
        used_j = 0
        while j>=0:
            if used+(target-flowers[j])<newFlowers:
                ans+=full
                used+=target-flowers[j]
                used_j+=target-flowers[j]
                j-=1
            else:
                break
        j+=1
        i = 0
        gardens = 0
        lower = 0
        while i<=j:
            if (i==j or flowers[i]!=lower):
                if gardens>0:
                    a = min(flowers[i],target-1) if i<j else target-1
                    if used + gardens*(a-lower)<=newFlowers:
                        used+=gardens*(a-lower)
                        lower = a
                    else:
                        b = (newFlowers-used)//gardens
                        used+=gardens*b
                        lower = b+lower
                        break
                else:
                    lower = flowers[i]
            if i==j:
                break
            gardens+=1
            i+=1
        final_ans = ans+(partial*lower if gardens>0 else 0)
        while j<end:
            used-=min(target-flowers[j],target-lower)
            used_j-=min(target-flowers[j],target-lower)
            ans-=full
            j+=1
            while i<=j:
                if (i==j or flowers[i]>lower):
                    if gardens>0:
                        a = min(flowers[i],target-1) if i<j else target-1
                        if used + gardens*(a-lower)<=newFlowers:
                            used+=gardens*(a-lower)
                            lower = a
                        else:
                            b = (newFlowers-used)//gardens
                            used+=gardens*b
                            lower = b+lower
                            break
                    else:
                        lower = flowers[i]
                if i==j:
                    break
                gardens+=1
                i+=1
            final_ans = max(final_ans,ans+(partial*lower if gardens>0 else 0))
        return final_ans+initial
870