Teleporters Path - Core idea

Core idea: You need an Euler path from level $1$ to level $n$.

Conditions for directed Euler path:

• Vertex $1$ (start): $\text{out-degree} = \text{in-degree} + 1$
• Vertex $n$ (end): $\text{in-degree} = \text{out-degree} + 1$
• All other vertices: $\text{in-degree} = \text{out-degree}$

If these conditions aren't met exactly, output "IMPOSSIBLE".

Also check: The graph must be connected (underlying undirected graph).