Statement

Giorgio is a big fan of board games and he has asked William to play with him. This time they are going to play a cooperative game, which means they need to play together in order to maximize their score. They have a lot of free time, so they are going to play T matches. The rules of the game are very simple. First of all, in the i-th match they choose a number N_i. Then, for each number from 1 to N_i they need to decide whether Giorgio or William keeps it. Let's call A the set of numbers given to Giorgio and B the set of numbers given to William. Let X_A be the bitwise xor of all the numbers in A and X_B the bitwise xor of all the numbers in B. The score of the match is given by the sum of X_A and X_B. What is the maximum score they can achieve in each match?