Three-Player Take-It-or-Leave-It Split

Players A, B, C divide $100 in integer dollars. A proposes a split (a, b, c) summing to 100. If B accepts, the split stands. If B rejects,$1 is burned (now $99 remain) and B proposes a split of the remaining money between B and C only; if C rejects that, another$1 is burned ($98 remain) and C takes everything. All players are rational, maximize their own dollars, and accept when indifferent. How many dollars does A keep in A's optimal proposal?