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 a[105];
map<int, int> sg, mp;
int getsg(int state) {
  if (state == 0) return 0;
  if (sg.find(state) != sg.end()) return sg[state];
  int mx = 0;
  for (int i = 1; i < 30; i++)
    if ((state >> i) & 1) mx = i;
  int vis = 0;
  for (int i = 1; i <= mx; i++) {
    int next_state = (state >> i) | (state & ((1 << i) - 1));
    vis |= (1 << getsg(next_state));
  }
  int res = 0;
  for (int i = 0; i <= 30; i++)
    if (~vis >> i & 1) {
      res = i;
      break;
    }
  return sg[state] = res;
}
int main() {
  int n;
  scanf("%d", &n);
  mp.clear();
  sg.clear();
  int ans = 0, ans1 = 0, _max = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    _max = max(a[i], _max);
  }
  for (int i = 1; i <= n; i++) {
    int p = a[i];
    for (int j = 2; j * j <= a[i]; j++) {
      int cnt = 0;
      if (p % j == 0) {
        while (p % j == 0) {
          cnt++;
          p /= j;
        }
        mp[j] |= (1 << cnt);
      }
    }
    if (p > 1) {
      mp[p] |= (1 << 1);
    }
  }
  map<int, int>::iterator it;
  it = mp.begin();
  for (; it != mp.end(); it++) {
    int i = it->second;
    if (i > 0) {
      ans ^= getsg(i);
    }
  }
  ans = ans ^ ans1;
  if (ans == 0)
    puts("Arpa");
  else
    puts("Mojtaba");
}
