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 const N = 2e6 + 5;
int n, u;
map<int, int> Max;
map<int, int> DP;
int CALC(int x) {
  if (DP.find(x) != DP.end()) return DP[x];
  int tmp[32] = {}, ans = 0;
  for (int i = 1; (1 << i) <= x; i++) {
    tmp[CALC((x >> i) | (x & ((1 << i) - 1)))] = 1;
  }
  while (tmp[ans]) ans++;
  return DP[x] = ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    cin >> u;
    for (int i = 2; i <= sqrt(u); i++) {
      int cnt = 0;
      while (u % i == 0) {
        u /= i;
        cnt++;
      }
      if (cnt == 0) continue;
      Max[i] |= (1 << cnt);
    }
    if (u > 1) Max[u] |= (1 << 1);
  }
  for (auto it : Max) {
    ans ^= CALC(it.second);
  }
  if (ans == 0) {
    cout << "Arpa";
  } else {
    cout << "Mojtaba";
  }
}
