|Codeforces Round #659 (Div. 1)|
Koa the Koala and her best friend want to play a game.
The game starts with an array $$$a$$$ of length $$$n$$$ consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to $$$0$$$. Koa starts.
Let's describe a move in the game:
More formally: if the current score of the player is $$$x$$$ and the chosen element is $$$y$$$, his new score will be $$$x \oplus y$$$. Here $$$\oplus$$$ denotes bitwise XOR operation.
Note that after a move element $$$y$$$ is removed from $$$a$$$.
At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw.
If both players play optimally find out whether Koa will win, lose or draw the game.
Each test contains multiple test cases. The first line contains $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Description of the test cases follows.
The first line of each test case contains the integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of $$$a$$$.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 10^9$$$) — elements of $$$a$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.
For each test case print:
3 3 1 2 2 3 2 2 3 5 0 0 0 2 2
WIN LOSE DRAW
4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4
WIN WIN DRAW WIN
In testcase $$$1$$$ of the first sample we have:
$$$a = [1, 2, 2]$$$. Here Koa chooses $$$1$$$, other player has to choose $$$2$$$, Koa chooses another $$$2$$$. Score for Koa is $$$1 \oplus 2 = 3$$$ and score for other player is $$$2$$$ so Koa wins.