Bessie likes downloading games to play on her cell phone, even though she does find the small touch  screen rather cumbersome to use with her large hooves. She is particularly intrigued by the current game she is playing. The game starts with a sequence of  N positive integers (2≤N≤262,144), each in the range 1…40. In one move, Bessie can take two adja cent numbers with equal values and replace them a single number of value one greater (e.g., she migh t replace two adjacent 7s with an 8). The goal is to maximize the value of the largest number presen t in the sequence at the end of the game. Please help Bessie score as highly as possible!