
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
There are $n$ students standing one behind the other in a circle, with heights $h_{1}<h_{2}<\ldots<h_{n}$. At any moment, if a student of height $h_{k}$ is directly behind a student of height less than or equal to $h_{k-2}$, they can choose to switch places with that student. Determine the maximum number of exchanges that can occur among all initial configurations and possible exchange choices.

Present the answer in LaTex format: \boxed{Your answer}
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