- Time limit: 1.00 s
- Memory limit: 512 MB
Your task is to find out who wins if both players play optimally.
Input
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.
Output
For each test case, print "first" if the first player wins the game and "second" if the second player wins the game.
Constraints
- $1 \le t \le 2 \cdot 10^5$
- $1 \le n \le 2 \cdot 10^5$
- $1 \le x_i \le 10^9$
- the sum of all $n$ is at most $2 \cdot 10^5$
Input:
3
4
5 7 2 5
2
4 1
3
4 4 4
Output:
first
first
second