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?

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.

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