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<unsigned int, int> N;
inline unsigned int f(unsigned int x, int k) {
  return (x & ((1 << (k - 1)) - 1)) | (x >> k);
}
int nim(unsigned int x) {
  auto itr = N.find(x);
  if (itr != N.end()) return itr->second;
  unsigned int mask = 0;
  for (int i = 1; i < 31; i++)
    if (f(x, i) != x) mask |= 1 << nim(f(x, i));
  for (int i = 0; i < 31; i++)
    if ((mask & (1 << i)) == 0) {
      N[x] = i;
      return i;
    }
}
map<int, unsigned int> M;
void factor(int x) {
  for (int i = 2; i * i <= x; i++) {
    int c = -1;
    while (x % i == 0) {
      x /= i;
      c++;
    }
    if (c >= 0) M[i] |= (1 << c);
  }
  if (x > 1) M[x] |= 1;
}
int main() {
  N[0] = 0;
  int n;
  scanf("%i", &n);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%i", &x);
    factor(x);
  }
  int res = 0;
  for (auto i : M) res ^= nim(i.second);
  puts(res == 0 ? "Arpa" : "Mojtaba");
}
