A Simple Nim

Two players take turns picking candies from n heaps,the player who picks the last one will win the game.On each turn they can pick any number of candies which come from the same heap(picking no candy is not allowed).To make the game more interesting,players can separate one heap into three smaller heaps(no empty heaps)instead of the picking operation.Please find out which player will win the game if each of them never make mistakes.

Intput contains multiple test cases. The first line is an integer $1\le T\le 100$, the number of test cases. Each case begins with an integer n, indicating the number of the heaps, the next line contains N integers $s[0],s[1], ....,s[n-1]$, representing heaps with $s[0],s[1], ...,s[n-1]$ objects respectively.$(1\le n\le 10^6,1\le s[i]\le 10^9)$

For each test case,output a line whick contains either"First player wins."or"Second player wins".

2
2
4 4
3
1 2 4

Second player wins.
First player wins.

UESTC

2016 Multi-University Training Contest 6