[Solution] Log Chopping solution codeforces

Log Chopping solution codeforces – There are 𝑛n logs, the 𝑖i-th log has a length of 𝑎𝑖ai meters. Since chopping logs is tiring work, errorgorn and maomao90 have decided to play a game.

[Solution] Log Chopping solution codeforces

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 22 pieces. If the length of the chosen log is 𝑥x, and the lengths of the resulting pieces are 𝑦y and 𝑧z, then 𝑦y and 𝑧z have to be positive integers, and 𝑥=𝑦+𝑧x=y+z must hold. For example, you can chop a log of length 33 into logs of lengths 22 and 11, but not into logs of lengths 33 and 0022 and 22, or 1.51.5 and 1.51.5.

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 𝑡t (1𝑡1001≤t≤100)  — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer 𝑛n (1𝑛501≤n≤50)  — the number of logs.

The second line of each test case contains 𝑛n integers 𝑎1,𝑎2,,𝑎𝑛a1,a2,…,an (1𝑎𝑖501≤ai≤50)  — the lengths of the logs.

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

[Solution] Log Chopping solution codeforces

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

Example
input

Copy
2
4
2 4 2 1
1
1
output

Copy
errorgorn
maomao90

Log Chopping solution codeforces

In the first test case, errorgorn will be the winner. An optimal move is to chop the log of length 44 into 22 logs of length 22. After this there will only be 44 logs of length 22 and 11 log of length 11.

After this, the only move any player can do is to chop any log of length 22 into 22 logs of length 11. After 44 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.

 

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