CF1672A.Log Chopping

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?

共有 $n$ 根原木，其中第 $i$ 根原木的长度为 $a_i$ 米。由于劈原木是一项非常辛苦的工作，errorgorn 和 maomao90 决定玩一个游戏。

errorgorn 和 maomao90 将轮流劈原木，errorgorn 先手。在自己的回合中，玩家需选择一根原木并将其劈成 $2$ 段。若所选原木长度为 $x$，劈出的两段长度分别为 $y$ 和 $z$，则 $y$ 与 $z$ 必须为正整数，且必须满足 $x = y + z$。例如，你可以将一根长度为 $3$ 的原木劈成长度分别为 $2$ 和 $1$ 的两段，但不能劈成长度为 $3$ 和 $0$、$2$ 和 $2$，或 $1.5$ 和 $1.5$ 的两段。

无法进行劈砍操作的玩家判负。假设 errorgorn 和 maomao90 均采取最优策略，那么谁将获胜？

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.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 100$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 50$），表示原木的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_1,a_2, \ldots, a_n$（$1 \leq a_i \leq 50$），表示各根原木的长度。

注意：所有测试用例的 $n$ 之和没有上界。

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

对于每个测试用例，如果 errorgorn 获胜，则输出 “errorgorn”；如果 maomao90 获胜，则输出 “maomao90”。（不带引号）

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.

在第一个测试用例中，errorgorn 将获胜。一种最优操作是将长度为 $4$ 的原木砍成两段长度均为 $2$ 的原木。此后，场上将仅剩 $4$ 段长度为 $2$ 的原木和 $1$ 段长度为 $1$ 的原木。

此后，双方玩家唯一可行的操作是将任意一段长度为 $2$ 的原木砍成两段长度均为 $1$ 的原木。经过 $4$ 次操作后，轮到 maomao90 行动，而他将无法再进行任何操作。因此 errorgorn 获胜。

在第二个测试用例中，errorgorn 在他的第一回合便无法进行任何操作，立即判负，故 maomao90 获胜。