Alice and Bob are playing a game called Moving Chips. The game is played on an board where some cells have some chips on it. Two players move alternately. Each turn consists of one person moving a chip to any cell to its left or any cell to its top. For example, the possible movements of chip A on a board is:
The last player who moves all the chips to the top left cell wins.
Consider the configuration of a board in this file. .
denotes an empty cell and a digit denotes the number of chips on that cell.
Alice will move first. Assume that both players move optimally, who will win the game?
Clarifications: