Human Pyramid

As chairman of the Building A Pyramid Committee, you are specialized in breaking one specific world record: building the highest human pyramid. Unfortunately, you only know a limited number of people who are willing to be in the pyramid. After all, building human pyramids does not make much money, so most people are volunteers.

A full human pyramid of height \(h\) consists of \(h\) layers of people. As seen from below, it has \(h\) people on the first layer, \(h-1\) on the second, \(h-2\) on the third, and so forth until eventually the final layer has just a single person. To determine whether you can break the world record, you need to know how high a pyramid you can build. Given how many people are available, how tall is the highest possible human pyramid that these people can make?

The input consists of:

• One line with an integer $n$ ($1 \leq n \leq 10^{12}$), the number of people available to build the pyramid.

Output the height of the highest possible pyramid you can build with $n$ people.