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;
const int N = 2e6 + 6, MODM = 1e9 + 7;
const long long INF = 1e18 + 9;
unordered_map<int, int> mask_prime;
unordered_map<int, int> was;
unordered_map<int, int> val;
long long get_grand(long long x) {
  if (was[x]) return val[x];
  unordered_set<int> q;
  for (int k = 1; k <= 31; ++k) {
    if ((1LL << k) <= x) {
      long long next_mask = ((x >> k) | (x & ((1 << (k)) - 1)));
      q.insert(get_grand(next_mask));
    }
  }
  long long res = 0;
  while (q.find(res) != q.end()) ++res;
  was[x] = 1;
  val[x] = res;
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  was[0] = 1;
  val[0] = 0;
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n; ++i) {
    int x = a[i];
    for (long long j = 2; j * j <= x; ++j) {
      if (x % j) continue;
      int cnt = 0;
      while (x % j == 0) {
        x /= j;
        ++cnt;
      }
      mask_prime[j] |= (1LL << cnt);
    }
    if (x > 1) {
      mask_prime[x] |= (1LL << 1);
    }
  }
  long long ans = 0;
  for (auto to : mask_prime) {
    ans ^= get_grand(to.second);
  }
  if (ans)
    cout << "Mojtaba\n";
  else
    cout << "Arpa\n";
  return 0;
}
