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**Task** | Statistics

Time limit: | 1.00 s | Memory limit: | 512 MB |

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.

- $1 \le t \le 5 \cdot 10^5$

- $1 \le n \le 5 \cdot 10^5$

- $1 \le x_i \le 10^9$

- the sum of all $n$ is at most $5 \cdot 10^5$

Input:

`3`

4

5 7 2 5

2

4 1

3

4 4 4

Output:

`first`

first

second