Now it's time for lunch. Today's menu is chocolate!
Though every baby likes chocolate, the appetites of babies are little. After lunch, there are still $n$ pieces of chocolate remained: The length of the $i$th piece is $l_i$.
Using the remained chocolate, Baby Volcano is going to play a game with his teacher, Mr. Sprague. The rule of the game is quite simple.
Two player plays in turns, and Baby Volcano will play first:
1. In each turn, the player needs to select one piece of chocolate. If the length of the selected piece is equal to $1$, the player of this turn will lose immediately.
2. Suppose the length of the selected piece is $l$. Then the player needs to select a positive integer $k$ satisfying $k$ is at least $2$ and $k$ is a factor of $l$.
3. Then the player needs to cut the selected piece into $k$ pieces with length $\frac{l}{k}$.
The game continues until one player selects a piece of chocolate with length $1$.
Suppose both players plays optimally, your task is to determine whether Baby Volcano will win.