Given a string colors, where each character is either white or black, wendy and bob play a game to manipulate this string as follows: a. they perform moves alternatively in turns and wendy makes the first move. b. in a single move, wendy can remove from the string any white character that has exactly 2 white neighbors. c. similarly, in a single move, bob can remove from string any black character that has exactly 2 black neighbors. d. when a character is removed, the strings shrink itself, so if a character y had neighbors x and z on its left and right respectively before the move, after the move is made, x and z become each other's neighbors. e. the first player who cannot perform a move loses the game. for example, if the colors string is with the first move wendy will change it to wwbb, and bob can no longer perform a move. determine who has a winning strategy assuming that both wendy and bob play optimally.