# Amazon Online Assessment (OA) 2021 - Storage Optimization

A company is experimenting with a flexible storage system for their warehouses. The storage unit consists of a shelving system
which is one meter deep with removable vertical and horizon separators. When all separators are installed,
each storage space is one cubic meter `(1' x 1' x 1')`

.
Determine the volume of the largest space when series of horizontal and vertical separators are removed.

### Example 1:

`n = 6`

`m = 6`

`h = [4]`

`v = [2]`

Consider the diagram below. The left image depicts the initial storage unit with `n = 6`

horizon and `m = 6`

Vertical separators,
where the volume of the largest storage space is `1 x 1 x 1`

.
The right image depicts that unit after the fourth horizon and second vertical separators are removed.
The maximum storage volume for that unit is then `2 x 2 x 1`

= `4`

cubic meters:

### Example 2:

#### Input:

`n = 3`

`m = 3`

`h = [2]`

`v = [2]`

#### Output: `4`

#### Explanation:

There are `n = m = 3`

separators in the vertical and horizontal directions. Separators to remove are `h = [2]`

and `v = [2]`

. so the unit looks like this:

Return the volume of the biggest space, `4`

, as the answer.

### Example 3:

#### Input:

`n = 3`

`m = 2`

`h = [1, 2, 3]`

`v = [1, 2]`

#### Output: `12`

#### Explanation:

Initially there are `n = 3`

horizontal and `m = 2`

vertical separators. Remove separators `h = [1, 2, 3]`

and `v = [1,2]`

. so the unit looks like this:

The volume of the biggest storage space is `12`

cubic meters.