A Simple Game

Chef is in need of money, so he decided to play a game with Ramsay. In this game, there are $N$ rows of coins (numbered $1$ through $N$). For each valid $i$, the $i$-th row contains $C_i$ coins with values $A_{i, 1}, A_{i, 2}, \ldots, A_{i, C_i}$. Chef and Ramsay alternate turns; Chef plays first. In each turns, the current player can choose one row that still contains coins and take one of the