Challenge: The Staircase Problem

Problem statement

Suppose a child is running up a staircase with $n$ steps and can hop either 1 step, 2 steps, or 3 steps at a time. Implement a function to count the number of possible ways that the child can run up the stairs.

Input

An integer that represents the number of stairs.

Output

An integer that represents the number of ways that those stairs can be climbed.

Sample input

n = 4;

Sample output

result = 7;

Coding challenge

First, take a close look at this problem and design a step-by-step algorithm before jumping to the implementation. This problem is designed for your practice, so try to solve it on your own first. If you get stuck, you can always refer to the solution provided in the solution section. Good luck!