Log Chopping

1000ms

262144K

Description:

There are $$$n$$$ logs, the $$$i$$$-th log has a length of $$$a_i$$$ meters. Since chopping logs is tiring work, errorgorn and maomao90 have decided to play a game.

errorgorn and maomao90 will take turns chopping the logs with errorgorn chopping first. On his turn, the player will pick a log and chop it into $$$2$$$ pieces. If the length of the chosen log is $$$x$$$, and the lengths of the resulting pieces are $$$y$$$ and $$$z$$$, then $$$y$$$ and $$$z$$$ have to be positive integers, and $$$x=y+z$$$ must hold. For example, you can chop a log of length $$$3$$$ into logs of lengths $$$2$$$ and $$$1$$$, but not into logs of lengths $$$3$$$ and $$$0$$$, $$$2$$$ and $$$2$$$, or $$$1.5$$$ and $$$1.5$$$.

The player who is unable to make a chop will be the loser. Assuming that both errorgorn and maomao90 play optimally, who will be the winner?

Input:

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of logs.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 50$$$) — the lengths of the logs.

Note that there is no bound on the sum of $$$n$$$ over all test cases.

Output:

For each test case, print "errorgorn" if errorgorn wins or "maomao90" if maomao90 wins. (Output without quotes).

Sample Input:

Sample Output:

errorgorn
maomao90

Note:

In the first test case, errorgorn will be the winner. An optimal move is to chop the log of length $$$4$$$ into $$$2$$$ logs of length $$$2$$$. After this there will only be $$$4$$$ logs of length $$$2$$$ and $$$1$$$ log of length $$$1$$$.

After this, the only move any player can do is to chop any log of length $$$2$$$ into $$$2$$$ logs of length $$$1$$$. After $$$4$$$ moves, it will be maomao90's turn and he will not be able to make a move. Therefore errorgorn will be the winner.

In the second test case, errorgorn will not be able to make a move on his first turn and will immediately lose, making maomao90 the winner.

Informação

Provedor Codeforces

Código CF1672A