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::unordered_map<int, int> dp;
int rec(int x) {
  if (dp.count(x)) return dp[x];
  if (x == 0) {
    dp[x] = 0;
    return 0;
  }
  std::unordered_set<int> s;
  for (int i = 1; i <= 30; ++i) {
    int y = (x >> i) | (x & ((1 << (i - 1)) - 1));
    if (y != x) s.insert(rec(y));
  }
  dp[x] = 0;
  while (s.count(dp[x])) ++dp[x];
  return dp[x];
}
int main(int argc, char* argv[]) {
  int n;
  scanf("%d", &n);
  std::vector<std::pair<int, int> > p;
  for (int i = 0; i < n; ++i) {
    int a;
    scanf("%d", &a);
    for (int x = 2; x * x <= a; ++x) {
      if (a % x == 0) {
        int cn = 0;
        while (a % x == 0) {
          ++cn;
          a /= x;
        }
        p.push_back(std::make_pair(x, cn));
      }
    }
    if (a > 1) p.push_back(std::make_pair(a, 1));
  }
  std::sort(p.begin(), p.end());
  int ans = 0;
  for (int i = 0, j = 0; i < p.size(); i = j) {
    int mask = 0;
    for (; j < p.size() && p[i].first == p[j].first; ++j)
      mask |= (1 << (p[j].second - 1));
    ans ^= rec((mask));
  }
  puts(ans ? "Mojtaba" : "Arpa");
  return 0;
}
