Czech ACM Student Chapter
Czech Technical University in Prague
Charles University in Prague
Technical University of Ostrava
acm
ˇ a
Slovak University of Technology
Pavol Jozef Saf´rik University in Koˇice
s
cz
ˇ
University of Zilina
Masaryk University
Matej Bel University in Bansk´ Bystrica
a
University of West Bohemia
CTU Open Contest 2018
Split Game
game.c, game.cpp, game.c11, Game.java, game.py
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 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 N piles with not necessarily 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 K which is smaller
than the size of the selected pile. Then the player splits the selected pile into as many piles of
size K 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 N (1 ≤ N ≤ 2000), the number of piles. The second line
contains a sequence of N integers Pi (1 ≤ Pi ≤ 2000), Pi represents the number of tokens in the
i-th pile.
Output Specification
Output a single line with either "First" or "Second", depending on which player wins the game
if both play optimally.
Output for Sample Input 1
Sample Input 1
3
First
123
Sample Input 2
Output for Sample Input 2
3
Second
122
