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;
string itos(int x) {
  stringstream ss;
  ss << x;
  return ss.str();
}
int xorsum, n, a[110];
map<int, int> grun;
int sieve[31700];
vector<int> p;
int mex(set<int> &s) {
  for (int i = 0;; i++)
    if (not s.count(i)) return i;
}
int getGrundy(int x) {
  if (grun.count(x)) return grun[x];
  if (x == 1) return grun[x] = 0;
  set<int> s;
  for (int i = 1; (1 << i) <= x; i++)
    s.insert(getGrundy(x >> i | (x & ((1 << i) - 1))));
  return grun[x] = mex(s);
}
void solve(int x) {
  int mask = 0;
  for (int i = 0; i < n; i++) {
    int cnt = 0;
    while (a[i] % x == 0) cnt++, a[i] /= x;
    mask |= (1 << cnt);
  }
  xorsum ^= getGrundy(mask);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 2; i < 31700; i++) {
    if (not sieve[i]) {
      p.push_back((i));
      for (int j = i * i; j < 31700; j += i) sieve[j] = 1;
    }
  }
  for (int i = 0; i < n; i++) {
    auto it1 = p.begin();
    while (a[i] > 1) {
      if (it1 == p.end()) {
        solve(a[i]);
        break;
      } else if (a[i] % *it1 == 0)
        solve(*it1);
      it1++;
    }
  }
  cout << (xorsum ? "Mojtaba" : "Arpa") << endl;
  return 0;
}
