For a long time, rich clientele of Binary Casino has been requesting a new way to gamble their money. To fulfill their wishes, the director of Binary Casino decided to introduce a new game called Split Your Tokens.
This game is played only when a customer is about to exit the casino. Instead of exchanging tokens won during his visit, he may take up the casino's challenge and bet all of his earned tokens on winning this game. Should the customer lose, all of his tokens are lost in favor of the casino.
When the game starts, the customer splits his tokens into piles with not necessarily the same
amount of tokens in each pile. The customer and the casino then exchange turns – in this game
we denote the customer as the first player and the casino as the second player. Each player in
his turn decides which pile he wants to split and chooses a positive integer
which is smaller
than the size of the selected pile. Then the player splits the selected pile into as many piles of
size
as possible. If any tokens remain, they form another pile on their own. A player loses
the game when he can not do any more splitting. The customer (first player) always plays first.
The director of Binary Casino is however not sure, whether this game will be profitable for the casino in the long term. Your task is thus to determine, for a given configuration of piles, which player wins when both players play optimally.
Input Specification
The first line contains one integer
, the number of piles. The second line
contains a sequence of
integers
,
represents the number of tokens in the
-th pile.
Output Specification
Output a single line with either First
or Second
, depending on which player wins the game
if both play optimally.
Sample Input 1
3
1 2 3
Sample Output 1
First
Sample Input 2
3
1 2 2
Sample Output 2
Second
Comments