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;
int N;
map<int, int> G;
map<int, vector<int>> Exps;
set<int> Primes;
string mask(int m) {
  string ret;
  for (int i = (0); i <= (31); i++)
    if (m & (1 << i))
      ret += '1';
    else
      ret += '0';
  return ret;
}
int grundy(int m) {
  if (G.find(m) != G.end()) return G[m];
  if (m == 0) return 0;
  set<int> used;
  for (int i = (1); i <= (31); i++) {
    int next = (m & ((1 << (i - 1)) - 1)) | (m >> i);
    if (next == m) continue;
    used.insert(grundy(next));
  }
  for (int i = 0; i >= 0; i++)
    if (used.find(i) == used.end()) return G[m] = i;
}
int main() {
  cin >> N;
  for (int i = (1); i <= (N); i++) {
    int x;
    scanf("%d", &x);
    for (int n = 2; n * n <= x; n++) {
      if (x % n == 0) {
        int e = 0;
        while (x % n == 0) x /= n, e++;
        Primes.insert(n);
        Exps[n].push_back(e);
      }
    }
    if (x > 1) Primes.insert(x), Exps[x].push_back(1);
  }
  int ans = 0;
  for (int p : Primes) {
    int mask = 0;
    for (int e : Exps[p]) mask |= (1 << (e - 1));
    ans ^= grundy(mask);
  }
  if (ans)
    cout << "Mojtaba";
  else
    cout << "Arpa";
}
