Given an integer array instructions, you are tasked with constructing a sorted array nums by inserting elements from instructions one by one, starting from an empty array nums.

For each element instructions[i] from left to right, insert it into nums such that nums remains sorted in nondecreasing order. The cost of inserting each element is defined as the minimum of:

• The number of elements currently in nums that are strictly less than instructions[i].

• The number of elements currently in nums that are strictly greater than instructions[i].

Return the total cost to insert all elements into nums. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ instructions.length $\leq 10^5$

• $1 \leq$ instructions[i] $\leq 10^5$

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.