Statement

Edoardo is organising the traditional New Year's Eve dinner of the OIS staff: after a round of well-stuffed pizzas, it will be desserts time! As everybody knows, this is a very delicate moment: everybody likes to order a dessert, but feels ashamed to do it. Thus, it is very easy to create a "Mexican standoff", where everyone is waiting for the others to take their move. More precisely, N staff members are attending the dinner. Member i (for i=0 … N-1) has M_i esteemed friends among the others, which we call F_i,j for j=0… M_i-1. Member i will feel allowed to take the dessert if and only if at least L_i of his esteemed friends have already done the same. After the waiter asks for desserts, members that are willing to order one will do so, possibly making other members order one for themself, until everybody that has not ordered a dessert does not feel allowed to do so. Help Edoardo plan the dinner budget by determining how many staff members will order a dessert!