Statement

During hard lockdown times, everyone's darkest side comes out from the mist! In Giorgio's case, that means compulsive and competitive cooking: he now wants to prepare the perfect pizza, and there's nothing that can stop him! However, achieving such a goal is not a simple matter, and he is still stuck on deciding the perfect balance of the N ingredients (numbered with i=0 … N-1). He found M trusted websites, numbered with j = 0 … M-1, each of them proposing different weights P_ij (in milligrams) for the various ingredients. The situation is made even more confusing by the fact that the doses on each website refer to a different total weight, and thus cannot be easily combined! To get out of the impasse, there is but one solution: convert each recipe to a total of 1 kg (10^6 mg), by multiplying each weight for an appropriate factor, and then average out all the resulting weights for each ingredient across the various recipes. Help Giorgio compute the perfect pizza recipe!