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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/**
 * @author Don Li
 */
public class GameWithMojtaba {
    
    Map<Integer, Integer> memo = new HashMap<>();
    
    void solve() {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = in.nextInt();
        
        Map<Integer, Integer> masks = new HashMap<>();
        for (int i = 0; i < n; i++) {
            int x = a[i];
            for (int p = 2; p * p <= x; p++) {
                if (x % p == 0) {
                    int k = 0;
                    while (x % p == 0) {
                        x /= p;
                        k++;
                    }
                    int mask = masks.getOrDefault(p, 0);
                    masks.put(p, mask | 1 << k - 1);
                }
            }
            if (x > 1) {
                int mask = masks.getOrDefault(x, 0);
                masks.put(x, mask | 1);
            }
        }
        
        int xor = 0;
        for (int mask : masks.values()) {
            xor ^= grundy(mask);
        }
        
        if (xor == 0) out.println("Arpa");
        else out.println("Mojtaba");
    }
    
    int grundy(int mask) {
        if (memo.containsKey(mask)) return memo.get(mask);
        
        long bits = 0;
        for (int i = 0; ; i++) {
            if (mask >> i == 0) break;
            int nmask = (mask >> i + 1) | (mask & (1 << i) - 1);
            int x = grundy(nmask);
            bits |= 1 << x;
        }
        
        int ret = Long.numberOfTrailingZeros(bits + 1);
        memo.put(mask, ret);
        return ret;
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new GameWithMojtaba().solve();
        out.close();
    }
    
    static FastScanner in;
    static PrintWriter out;
    
    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;
        
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
        
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
        
        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
