There are $n$ heaps of sticks and two players who move alternately. On each move, a player chooses a non-empty heap and removes $1$ , $2$ , or $3$ sticks. The player who removes the last stick wins the game.
Your task is to find out who wins if both players play optimally.
The first input line contains an integer $t$ : the number of tests. After this, $t$ test cases are described:
The first line contains an integer $n$ : the number of heaps.
The next line has $n$ integers $x_1,x_2,\ldots,x_n$ : the number of sticks in each heap.
For each test case, print "first" if the first player wins the game and "second" if the second player wins the game.
3 4 5 7 2 5 2 4 1 3 4 4 4\n \n · · · \n \n · \n \n · · \n
first first second\n \n \n