Statement

Since last time, William became very skeptical about Bitcoin. Its value is just too changeable! People will never use it if they can't be sure of its value. For this reason, William intends to fake some historical data in order to convince people that Bitcoin is slowly converging to some final value. He can only delete the historical entry of some days: he cannot add or change the data, someone will notice it! We say that a sequence of prices is converging when: (1) It's alternating (switching between "highs" and "lows"). (2) Its highs are decreasing (if the price hits a high of 1000€, the next high will be at most 999€). (3) Its lows are increasing (if the price hits a low of 100€, the next low will be at least 101€). For example, let's assume that William has the history of 7 price changes: 600, 400, 800, 1500, 700, 900, 800 In this case, William could fake the data like this: (1) Delete the historical entry with price 600. (2) Delete the historical entry with price 800...