codeforces 850C Arpa and a game with Mojtaba

Posted 2020-10-14

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.

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 a1, a2, ..., an (1 ≤ ai ≤ 109) — 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 = 17and k = 2, then Arpa chooses p = 17 and k = 1 and wins.

 

每个质因子分开做，局面数量不多，枚举决策暴力求sg值

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