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> mp, sg;
int n, ans;
inline void work(int x) {
  for (int i = 2, t; i * i <= x; ++i) {
    if (x % i == 0) {
      t = 1;
      x /= i;
      while (x % i == 0) ++t, x /= i;
      mp[i] |= 1 << (t - 1);
    }
  }
  if (x != 1) mp[x] |= 1;
}
int SG(int x) {
  if (x == 0) return 0;
  if (sg.count(x)) return sg[x];
  map<int, bool> vis;
  int a = x, t = 0;
  while (a) ++t, a >>= 1;
  for (int i = 1; i <= t; ++i)
    vis[SG((x >> i) | (x & ((1 << (i - 1)) - 1)))] = 1;
  for (int i = 0;; ++i)
    if (!vis[i]) return sg[x] = i;
}
int main() {
  scanf("%d", &n);
  for (int i = 1, t; i <= n; ++i) {
    scanf("%d", &t);
    work(t);
  }
  for (map<int, int>::iterator it = mp.begin(); it != mp.end(); ++it)
    ans ^= SG(it->second);
  printf(ans ? "Mojtaba\n" : "Arpa\n");
  return 0;
}
