Tesla Pyramid

Problem Statement:

Elon Musk wants to build a pyramid of Teslas to appease the Martian Gods. If a pyramid has a height of K units, then there are i Teslas on the ith level (1 ≤ i ≤ K). To avoid being killed by the Martians when the SpaceX astronauts land on Mars, Elon Musk has hired you to find the maximum height pyramid that can be formed using N Teslas.

Constraints:

Subtask 1: 20 points

• 1 ≤ N ≤ 10⁵

Subtask 2: 60 points

• 1 ≤ N ≤ 10⁹

Input format:

• The first line contains a single integer N, the number of coins.

Output format:

• Print a single integer K, the height of the largest pyramid that you can form.

Sample input:

7 

Sample output:

3