MHB How Does the Number of Metro Stations Affect the Color of Connecting Lines?

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In a city with n Metro stations arranged in a circular path, each nearest pair is connected by a blue line, while all other pairs are connected by red lines. The discussion explores the relationship between the number of blue and red lines, establishing that the number of red lines is 99 times that of blue lines. For n=4, there are 4 blue lines and 6 red lines, while for n=5, there are 5 blue lines and 10 red lines. The thread seeks to generalize this for any integer n greater than 2. Understanding this relationship is crucial for analyzing the connectivity of the Metro system.
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Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is
 
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Let's pick n=4.
How many blue lines and how many red lines?
What if n=5?
How many for an arbitrary n?
 

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