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;
map<vector<int>, int> grundy;
int g(vector<int> v) {
  int i, j;
  sort(v.begin(), v.end());
  if (grundy.find(v) != grundy.end()) return grundy[v];
  set<int> s;
  if (v.size())
    for (i = 1; i <= v.back(); ++i) {
      vector<int> vv;
      for (j = 0; j < v.size(); ++j)
        if (v[j] > i)
          vv.push_back(v[j] - i);
        else if (v[j] && v[j] != i)
          vv.push_back(v[j]);
      s.insert(g(vv));
    }
  i = 0;
  while (s.find(i) != s.end()) i++;
  return grundy[v] = i;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  unordered_map<int, int> f[101], mp;
  unordered_map<int, int>::iterator it;
  int n, a[101], i, ans = 0, j, c = 0;
  cin >> n;
  for (i = 0; i < n; ++i) cin >> a[i];
  for (i = 0; i < n; ++i) {
    for (j = 2; j * j <= a[i]; ++j)
      if (a[i] % j == 0) {
        c = 0;
        while (a[i] % j == 0) {
          a[i] /= j;
          c++;
        }
        f[i][j] = c;
        mp[j] = 1;
      }
    if (a[i] != 1) f[i][a[i]] = 1, mp[a[i]] = 1;
  }
  for (it = mp.begin(); it != mp.end(); it++) {
    vector<int> v;
    for (i = 0; i < n; ++i) v.push_back(f[i][it->first]);
    ans ^= g(v);
  }
  if (ans)
    cout << "Mojtaba";
  else
    cout << "Arpa";
  return 0;
}
