In a country with n cities, there is a recurrent one -way flight between every pair of cities. Every flight has a constant price in the range $100, $120, $140, $160, $180.

A $N flight ticket gives unlimited access to flights that cost $N, and tickets can be traded for tickets of lower prices.

For example, with a $160 ticket, Brad could take a $160 ticket, trade his ticket for a $120 ticket, then take a $120 flight.

Alice loves flying and wonders how many successive flights she can take with one ticket.

Determine the minimum value of n needed to guarantee, that she can take 4 such flights.