# Moving Chips (Large Input)

**Computer Science**Level 3

Alice and Bob are playing a game called *Moving Chips*. The game is played on an \(n \times m\) 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 \(3\times 5\) board is:

The last player who moves all the chips to the top left cell wins.

Consider the configuration of a \(100\times 100\) 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**:

- The chips can be stacked on top of each other.
- Only one chip may be moved at a time (not a stack), but a chip can move any number of spaces in a single direction (left or up).
- The chips can move passing any chips.

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