Problem Statement  
Alan and Bob are playing a game with two piles of sticks. The two players alternate turns, and Alan gets the first turn. During each turn, the player must remove exactly n^2 sticks from each pile, where n is some positive integer. The value of n does not have to be the same for each pile.
For example, he can remove 1^2 = 1 stick from the first pile and 3^2 = 9 sticks from the second pile. The first player who cannot make a valid move is declared the loser. The first pile initially contains size0 sticks and the second pile contains size1 sticks. Suppose both players play optimally. One of them has a winning strategy (no matter how his opponent plays he can always win) and he wants to win as fast as possible. The other player wants to lose as slowly as possible. Return a String formatted as "<WINNER> will win after <NUMBER> moves" (quotes for clarity), where <WINNER> is the name of the winner and <NUMBER> is the total number of turns in the game. The total number of turns is the sum of all the successful turns taken by Alan and Bob.  
Definition  
 
Constraints  
  size0 and size1 will each be between 1 and 10000, inclusive.  
Examples  
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