<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 We will call a "staircase" a figure consisting of cells arranged in a step-like shape (see the picture for examples of staircases with 7 and 8 cells). In the drawing of a staircase, we will add markings: we will outline several non-overlapping sides of the cells in red so that each vertex of each cell belongs to exactly one red segment. How many different markings are there for a staircase consisting of 200 cells? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
201
We will call a "staircase" a figure consisting of cells arranged in a step-like shape (see the picture for examples of staircases with 7 and 8 cells). In the drawing of a staircase, we will add markings: we will outline several non-overlapping sides of the cells in red so that each vertex of each cell belongs to exactly one red segment. How many different markings are there for a staircase consisting of 200 cells?
test