MathNet 2012 Question 3

$N$ boys ($N \ge 3$), no two of them having the same height, are arranged along a circle. A boy in the given arrangement is said to be *tall* if he is taller than both of his neighbors; a boy is said to be *short* if he is shorter than both of his neighbors.
Prove that the number of tall boys is equal to the number of short boys in any arrangement of the boys along the circle.