Case: Stairs

Clue of $N$

A half-lane with a clue of $N$ must have the solution $\text{| 1 2 3 ... } (N-1) \ N$ .


N						.


N	1	2	…	N-1	N	.

Examples








		5



		5
		4
		3
		2
		1
		5

Explanation

An $N$ -clue means we can see $N$ skyscrapers, so all the skyscrapers are visible. The only ordering that achieves this is where all the skyscrapers are in ascending order.

Any other ordering, and we wouldn’t be able to see all the skyscrapers – we’d have a taller one blocking a shorter one behind it!