A11077 | Arpa and a game with Mojtaba

Mojtaba and Arpa are playing a game. They have a list of $n$ numbers in the game.

In a player's turn, he chooses a number $p^{k}$ (where $p$ is a prime number and $k$ is a positive integer) such that $p^{k}$ divides at least one number in the list. For each number in the list divisible by $p^{k}$ , call it $x$ , the player will delete $x$ and add  to the list. The player who can not make a valid choice of $p$ and $k$ loses.

Mojtaba starts the game and the players alternatively make moves. Determine which one of players will be the winner if both players play optimally.

The first line contains a single integer $n$ ( $1<=n<=100$ ) — the number of elements in the list.

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ) — the elements of the list.

If Mojtaba wins, print "Mojtaba", otherwise print "Arpa" (without quotes).

You can print each letter in any case (upper or lower).