Score : 1000 points
There are N integers written on a blackboard. The i-th integer is A_i, and the greatest common divisor of these integers is 1.
Takahashi and Aoki will play a game using these integers. In this game, starting from Takahashi the two player alternately perform the following operation:
The player who is left with only 1s on the blackboard and thus cannot perform the operation, loses the game. Assuming that both players play optimally, determine the winner of the game.
The input is given from Standard Input in the following format:
N A_1 A_2 … A_N
If Takahashi will win, print First
. If Aoki will win, print Second
.
3 3 6 7
First
Takahashi, the first player, can win as follows:
4 1 2 4 8
First
5 7 8 8 8 8
Second