Where ice cream really comes from.

Contrary to common belief, ice cream isn't manufactured in factories or shops. All ice cream in the world comes from a single island, named IceCreamLand, which is off the coast of... well... it's right in the middle of the ocean!

Queen Jane, who had the throne of IceCreamLand, recently succumbed to her death from Diabetes (no wonder). Prince Jack, has now ascended to the throne, and has made a large number of changes to how the island operates. The people of IceCreamLand are simpletons, just like Prince Jack.

Remember IceCreamLand the next time you're licking a nice cone of ice cream. Pic credits: Clipart Library

Ice Cream is manufactured in small houses, and then packed in large boxes, which are in the shape of a cube . The boxes can be made in any size needed, but the units used are $spoons$ , which is the length of the standardized spoon in IceCreamLand.

When it comes to surveying ice cream exports, Prince Jack has to use whatever little maths he knows, which is quite very little. IceCreamLand exports ice cream to a variety of customers; everyone buys the ice cream per box, but the way they price the box is different. Some customers buy the ice cream based on the surface area of the box, while some buy it based on the volume of the box. John, the box manufacturer, has the skills to create a box with a specific volume, even though he has no math education!

To serve the different customers, Queen Jane used to convert the volume of the box to it's surface area; this maths is not known to anyone in IceCreamLand, not even Prince Jack. To solve the problem, John has been ordered to create special boxes, such that, the volume of the box, is equal to the surface area of the box as well (Jack doesn't really know the difference between $spoons$ and $spoons^2$ ).

John can make a box only if he knows it's volume. But, a special box, which has the same magnitude of surface area and volume, is something which no one has seen before (or they probably never realized it). You've been promised a special box of ice cream if you can figure out what the volume of the special box is!

Type in the volume of the special box as the answer. If no special boxes exist, enter $-1$ . If there are multiple special boxes, you obviously want the one with the most ice cream! In such a case, enter the volume of the special box which has the greatest volume under $10^4$ .

Notes:

• All special boxes must have their side as a natural number; thus, the volume will also be a natural number.
• Volume of cube with side $s$ : $s^3$ .
• Surface area of cube with side $s$ : $6s^2$ .