Code Submission Evaluation System | Login |

**Task** | Statistics

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

There is a staircase that consists of $n$ stairs, numbered $1,2,\ldots,n$. Initially, each stair has some number of balls.

There are two players who move alternately. On each move, a player chooses a stair $k$ where $k \neq 1$ and it has at least one ball. Then, the player moves any number of balls from stair $k$ to stair $k-1$. The winner is the player who moves last.

Your task is to find out who wins the game when both players play optimally.

The first input line has an integer $t$: the number of tests. After this, $t$ test cases are described:

The first line contains an integer $n$: the number of stairs.

The next line has $n$ integers $p_1,p_2,\ldots,p_n$: the initial number of balls on each stair.

For each test, print "first" if the first player wins the game and "second" if the second player wins the game.

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

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

- $0 \le p_i \le 10^9$

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

Input:

`3`

3

0 2 1

4

1 1 1 1

2

5 3

Output:

`first`

second

first