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>
std::mt19937 rng(
    (int)std::chrono::steady_clock::now().time_since_epoch().count());
std::vector<std::pair<int, int> > factors(int x) {
  std::vector<std::pair<int, int> > ans;
  for (int i = 2; i * i <= x; i++) {
    int e = 0;
    while (x % i == 0) {
      x /= i;
      e++;
    }
    if (e > 0) {
      ans.emplace_back(i, e);
    }
  }
  if (x > 1) {
    ans.emplace_back(x, 1);
  }
  return ans;
}
std::map<int, int> memo;
int dp(int mask) {
  if (mask == 0) return mask;
  if (memo.count(mask)) return memo[mask];
  int ha = 0;
  for (int i = 0; (1 << i) <= mask; i++) {
    ha |= 1 << dp((mask >> (i + 1)) | (mask & ((1 << i) - 1)));
  }
  int ans = 0;
  while (ha & (1 << ans)) ans++;
  return memo[mask] = ans;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);
  int n;
  std::cin >> n;
  std::map<int, int> wtf;
  while (n--) {
    int x;
    std::cin >> x;
    auto got = factors(x);
    for (auto p : got) {
      wtf[p.first] |= 1 << (p.second - 1);
    }
  }
  int nim = 0;
  for (auto p : wtf) {
    nim ^= dp(p.second);
  }
  std::cout << (nim == 0 ? "Arpa\n" : "Mojtaba\n");
}
