Two pirates A and B stole 100 gold coins. They split it as follows: A takes a pile of n coins (left over from the undistributed coins) and B chooses who gets the pile. If there are still coins left over (not distributed) after either A or B gets nine piles, then whoever did not get nine piles take the leftover coins. suppose A and B do this in an optimum ways (such as to maximize their profits), what is the number of coins A gets? justify.