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 <image> 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.
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;

/**
 * Created by Pranav ps on 06-09-2017.
 */
public class ArpaAndGame {
    private static HashSet<Integer> primes;
    private static HashMap<Integer,Integer> grundy;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[n];
        primes = new HashSet<>();
        grundy = new HashMap<>();
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
            deal(arr[i]);
        }

        int res = 0;
        for(int p: primes){
            int local = 0;
            for (int i = 0; i < n; i++) {
                int k = 0;
                while(arr[i]%p==0) {
                    k++;
                    arr[i]/=p;
                }
                local |= 1<<k;
            }
            res^=f(local);
        }
        if(res==0)
            System.out.println("Arpa");
        else
            System.out.println("Mojtaba");
    }

    private static int f(int n) {
        if(grundy.containsKey(n))
            return grundy.get(n);

        if(n==1){
            grundy.put(n,0);
            return 0;
        }

        HashSet<Integer> toMex = new HashSet<>();

        for(int i = 1; (n>>i) > 0; i++){
            toMex.add(f((n>>i)|(n&((1<<i) - 1))));
        }

        grundy.put(n,mex(toMex));
        return grundy.get(n);

    }

    private static Integer mex(HashSet<Integer> toMex) {
        int i = 0;
        while(true){
            if(!toMex.contains(i))
                return i;
            i++;
        }
    }

    private static void deal(int num) {
        int numC = num;
        for(int p = 2; p*p <= numC; p++){
            if(num%p == 0)
                primes.add(p);
            while(num%p == 0)
                num/=p;
        }
        if(num!=1)
            primes.add(num);
    }
}
