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There are n logs, the i-th log has a length of ai 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≤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 n (1≤n≤50) — the number of logs.

The second line of each test case contains n integers a1,a2,…,an (1≤ai≤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).

2291: Log Chopping

Description

Input

Output

Sample Input Copy

Sample Output Copy

Source/Category