Problem Brief

Product of the Maximum and Minimum in a Dataset

INTERNFULLTIMEOA

Starting with an empty set of integers named elements, perform the following query operations:

The command push x inserts the value of x into elements.
The command pop x removes the value of x from elements.

The integers in elements need to be ordered in such a way that after each operation is performed, the product of the maximum and minimum values in the set can be easily calculated.

Function Description

Complete the function maxMin in the editor below.

maxMin has the following parameter(s):

s[n]: an array of operations strings
int x[n]: an array of x where x[i] goes with operations[i].

Returns

int[n]: an array of long integers that denote the product of the maximum and minimum of elements after each query

1Example 1

Input

operations = ["push", "push", "push", "pop"], x = [1, 2, 3, 1]

Output

[1, 2, 3, 6]

Explanation

Visualize elements as an empty multiset, elements = {}, and refer to the return array as products. The sequence of operations occurs as follows:

push 1 → elements = {1}, so the minimum = 1 and the maximum = 1. Then store the product as products[0] = 1 × 1 = 1.
push 2 → elements = {1, 2}, so the minimum = 1 and the maximum = 2. Then store the product as products[1] = 1 × 2 = 2.
push 3 → elements = {1, 2, 3}, so the minimum = 1 and the maximum = 3. Then store the product as products[2] = 1 × 3 = 3.
pop 1 → elements = {2, 3}, so the minimum = 2 and the maximum = 3. Then store the product as products[3] = 2 × 3 = 6.

Return products = [1, 2, 3, 6]

Constraints

Limits and guarantees your solution can rely on.

1 ≤ n ≤ 10^5
1 ≤ x[i] ≤ 10^9
It is guaranteed that each operations[i] is either push or pop.
It is guaranteed that any value popped will exist in the array.