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 K = 20;
int val[1 << K];
map<int, int> mem;
int get(int mask) {
  if (mem.count(mask)) return mem[mask];
  vector<int> vec(35, 0);
  for (int i = 0; i < 30; i++) {
    if (mask >= (1 << i)) {
      int nmask = mask & ((1 << i) - 1);
      nmask = nmask | (mask >> (i + 1));
      vec[get(nmask)] = 1;
    }
  }
  int ret = 35;
  for (int i = 0; i < 35; i++) {
    if (vec[i] == 0) {
      ret = i;
      break;
    }
  }
  return mem[mask] = ret;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  map<int, vector<int> > mp;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    for (int y = 2; y * y <= x; y++) {
      int cnt = 0;
      while (x % y == 0) {
        cnt++;
        x /= y;
      }
      if (cnt) mp[y].push_back(cnt);
    }
    if (x > 1) mp[x].push_back(1);
  }
  int ret = 0;
  for (auto &pp : mp) {
    int mask = 0;
    for (auto x : pp.second) {
      mask |= (1 << (x - 1));
    }
    ret ^= get(mask);
  }
  if (ret)
    cout << "Mojtaba" << '\n';
  else
    cout << "Arpa" << '\n';
  return 0;
}
