Alice has a collection of gardens represented by an integer array flowers, where flowers[i] denotes the number of flowers currently planted in the $i^{th}$ garden. She is given an additional newFlowers flowers that she can plant across any of the gardens. She can plant any number of additional flowers in each garden, provided the total number of newly planted flowers does not exceed newFlowers.

A garden is defined as complete if it contains at least target flowers. Otherwise, it is considered incomplete.

The total beauty of the gardens is calculated as the sum of:

• The number of complete gardens multiplied by full

• The minimum number of flowers among all incomplete gardens multiplied by partial

If there are no incomplete gardens, the second term contributes $0$ to the total beauty.

Return the maximum possible total beauty Alice can achieve.

Constraints:

• $1 \leq$ flowers.length $\leq 10^5$

• $1 \leq$ flowers[i], target $\leq 10^5$

• $1 \leq$ newFlowers $\leq 10^{10}$

• $1 \leq$ full, partial $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.