Statement

Davide wants to decorate his home for Christmas, even though his budget as a student is pretty limited, and he needs to avoid excessive expenses. After days of searching around the city, he finally found a nice row of almost new Christmas lights: it is time to start the decorations! The row consists of N consecutive lights, numbered from 0 to N-1. Each light has a colour L_i (i = 0 … N-1), represented by a number between 0 and C-1. Every colour between 0 and C-1 appears at least once in the row of lights. In order to save energy (running the house dynamo is tiring!), he wants to cut off a segment of consecutive lights from the row containing every colour between 0 and C-1 at least once. What is the length of the shortest segment he can cut?