CF2261C I Know About a Million Things

[月葬 - 黒魔 × rintaro soma](https://www.youtube.com/watch?v=4Mch-fZYQX8) Moggity and Larpity are playing a game with an array $ a_1, a_2, \ldots, a_n $ of positive integers. Moggity moves first, and then the players alternate turns. On their turn, a player chooses a non-empty set of positions of the array and removes the elements at these positions. Such a move is allowed only if at least one of the following conditions holds: - exactly one element is removed; - the sum of the removed elements is even. A player who cannot make a move loses. In other words, the player who faces an empty array loses. Determine which player has a winning strategy.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 1\,000\,000 $ ) — the length of the array. The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 1\,000\,000 $ ) — the elements of the array. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 1\,000\,000 $ .

For each test case, print "Moggity" if Moggity has a winning strategy, and "Larpity" otherwise. You can output the answer in any case (upper or lower). For example, the strings "MoggItY", "MOGGITY", "moggity", and "mOGGity" will be recognized as a win for Moggity.

In the first test case, Moggity removes the only element, and Larpity faces an empty array. In the second test case, Moggity cannot remove both elements at once, because $ 2 + 3 = 5 $ is odd. Whichever single element he removes, Larpity removes the remaining one, and then Moggity faces an empty array. Therefore, Larpity wins.