21088번 - Remove the Prime 출처다국어분류

Two players play a game using an array of positive integers. They make alternating moves, the player who cannot make a move loses. In one move you have to choose a prime number $p$ and a non-empty segment $[l;r]$ of the array such that all numbers in this segment are divisible by $p$, and then remove all factors $p$ from each of them. Removing all factors means that we take a number and divide it by $p$ while it is divisible.

Determine who wins if both players play optimally.

The first line contains one integer $n$ ($1 \le n \le 1000$) --- the size of array.

The second line contains the array $a_{1}, a_{2}, \ldots, a_{n}$ itself ($1 \le a_{i} \le 10^{18}$).

Print "First" (without quotes) if first player wins and "Second" (without quotes) otherwise.