Please dont usa AI$.$ Help me solve this Prob. $8$: A Dynamic Programming Exercise

Problem Statement: You are given a staircase with $n$ steps. You can climb the staircase in either of two ways at each step:

Climb $1$ step

Climb $2$ steps

Write a dynamic programming algorithm to determine the number of distinct ways you can climb to the top of the staircase.

Input: An integer $n($the total number of steps in the staircase$).$

Output: An integer representing the number of distinct ways to reach the top of the staircase.