You are a professional Python developer. Solve the following problem using Python. 
There is a staircase with a known number of steps. At each step we can step on each rung or step over one, passing 2 rungs at once in one step. We need to find the number of ways we can climb the stairs.

For example, if the staircase has 4 steps, the options are:

1→1→1→1

1→1→2

1→2→1

2→1→1

2→2

The solution must be as effective as possible.

Afterwards, check the script for errors and correct them if necessary. Your entire response should be in English, and in all capital letters.
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