Log Chopping

题意翻译

errorgorn 和 maomao90 在玩切木棍的游戏。 现在有 $n$ 根木棍，每次操作的时候，任意一方可以选择一根木棍，并将它切成两段，但必须满足切完之后任意一段长度均为正整数。 即长度为 $3$ 的木棍，可以切成长度为 $2$ 和 $1$ 的木棍，但不能切成 $3$ 和 $0$ 或 $1.5$ 和 $1.5$。 若哪一方不能再切木棍为输，请你判断双方采取最优的策略谁会赢。 注意：每个测试点共有 $t$ 组数据，开始时 errorgorn 先手。

题目描述

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?

输入输出格式

输入格式

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.

输出格式

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

输入输出样例

输入样例 #1

2
4
2 4 2 1
1
1

输出样例 #1

errorgorn
maomao90

说明

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.