Statement

As vaccinations against COVID-19 are starting all over the world, people seem to keep forgetting the one and only piece of advice they have been given in the last months: "Do Not Gather!". To receive their dose, people usually queue up outside the administration center and form a line. Often, though, the minimum interpersonal distance D (measured in centimeters) imposed by law is not respected, enabling possible infections. Luca was walking and accidentally noted the troubling situation: out of N people in queue at positions P_i, also measured in centimeters starting from the vaccination center, many seem to be in a risky position. How many pairs of people do not respect the distance, i.e. the distance between them is less than the required distance?