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C. Arpa and a game with Mojtaba

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMojtaba 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.

Input

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.

Output

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

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

Examples

Input

4

1 1 1 1

Output

Arpa

Input

4

1 1 17 17

Output

Mojtaba

Input

4

1 1 17 289

Output

Arpa

Input

5

1 2 3 4 5

Output

Arpa

Note

In the first sample test, Mojtaba can't move.

In the second sample test, Mojtaba chooses *p* = 17 and *k* = 1, then the list changes to [1, 1, 1, 1].

In the third sample test, if Mojtaba chooses *p* = 17 and *k* = 1, then Arpa chooses *p* = 17 and *k* = 1 and wins, if Mojtaba chooses *p* = 17 and *k* = 2, then Arpa chooses *p* = 17 and *k* = 1 and wins.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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