A 10-digit arrangement $0,1,2,3,4,5,6,7,8,9$ is called beautiful if:
1. When read from left to right, $0,1,2,3,4$ form an increasing sequence.
2. $5,6,7,8,9$ form a decreasing sequence.
3. $0$ is not the leftmost digit.

For example, $9807123654$ is a beautiful arrangement.

Determine the number of beautiful arrangements.

Let's think step by step and output the final answer within \boxed{}.
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