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.
#include <bits/stdc++.h>
using namespace std;
unordered_map<int, int> ans, mp;
int solve(int x) {
  if (ans.count(x) != 0) return ans[x];
  vector<bool> temp(32);
  for (int i = 0; (1 << i) <= x; i++) {
    temp[solve((x & ((1 << i) - 1)) | (x >> (i + 1)))] = true;
  }
  int ct = 0;
  while (temp[ct]) ct++;
  ans[x] = ct;
  return ct;
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int temp;
    cin >> temp;
    for (int j = 2; j * j <= temp; j++) {
      int c = 0;
      while (temp % j == 0) {
        temp /= j;
        c++;
      }
      if (c) mp[j] |= (1 << (c - 1));
    }
    if (temp > 1) mp[temp] |= (1);
  }
  int a = 0;
  ans[0] = 0;
  unordered_map<int, int>::iterator it = mp.begin();
  for (; it != mp.end(); it++) {
    a = a ^ solve((*it).second);
  }
  if (a == 0)
    cout << "Arpa" << endl;
  else
    cout << "Mojtaba" << endl;
}
