Problem G
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?
Input
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
Output the height of the highest possible pyramid you can build with $n$ people.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 |
2 |
| Sample Input 2 | Sample Output 2 |
|---|---|
12 |
4 |
