Trains

When a train travels from one station to another, stopping at all stations in between is too time-consuming. The Japanese tackled this issue with a simple idea: skip some of the stations!

The FUTSŪ train stops at every station.
The KAISOKU train skips some stations.
The KYŪKŌ train skips more stations.
The TOKKYŪ train skips most stations, only stopping at the biggest stations.

Consider a hypothetical map below:

Alice is currently at the $1^\text{st}$ station and would like to travel with the fewest stops possible. She came up with a simple method:

Take the fastest train to the nearest station without passing the desired station. Repeat this procedure until reaching the desired station.

However, this algorithm does not always give the fewest stops. Which station can be traveled with fewer stops than the proposed algorithm requires?

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For example, this is how Alice would travel to the $6^\text{th}$ station:

• Take KYŪKŌ train from the $1^\text{st}$ station to the $5^\text{th}$ station.
• Take FUTSŪ train from the $5^\text{th}$ station to the $6^\text{th}$ station.