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;
map<int, int> M;
int grundy(int a) {
  if (M.count(a)) return M[a];
  vector<int> tmp;
  for (int p = 1; (a >> p) != 0; ++p) {
    int lh = a & ((1 << p) - 1);
    int uh = (a >> p);
    tmp.push_back(grundy(lh | uh));
  }
  int gr = 0;
  sort(tmp.rbegin(), tmp.rend());
  while (tmp.size() && gr == tmp.back()) {
    while (tmp.size() && gr == tmp.back()) tmp.pop_back();
    ++gr;
  }
  return M[a] = gr;
}
map<int, int> pr;
void load(int a) {
  for (int p = 2; p * p <= a; ++p) {
    int pw = 0;
    while (a % p == 0) ++pw, a /= p;
    if (pw) pr[p] |= 1 | (1 << pw);
  }
  if (a != 1) pr[a] |= 3;
}
int main() {
  M[1] = 0;
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    int a;
    scanf("%d", &a);
    load(a);
  }
  int nim = 0;
  for (auto &p : pr) {
    nim ^= grundy(p.second);
  }
  if (nim == 0)
    printf("Arpa\n");
  else
    printf("Mojtaba\n");
}
