Mighty Friend

Motu and Tomu are very good friends who are always looking for new games to play against each other and ways to win these games. One day, they decided to play a new type of game with the following rules: - The game is played on a sequence $A_0, A_1, \dots, A_{N-1}$. - The players alternate turns; Motu plays first, since he's earlier in lexicographical order. - Each player has a score. The initial