#D504. Arpa and a game with Mojtaba
Arpa and a game with Mojtaba
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 pk (where p is a prime number and k is a positive integer) such that pk divides at least one number in the list. For each number in the list divisible by pk, 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 = 17 and k = 2, then Arpa chooses p = 17 and k = 1 and wins.
inputFormat
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.
outputFormat
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.
样例
4
1 1 1 1
Arpa