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;
const int mod = 1e9 + 7;
const int mx = INT_MAX;
const long double pi = 4 * atan((long double)1);
unordered_map<int, int> mask, game;
int grundy(int mask) {
  if (!mask) return 0;
  if (game.count(mask)) return game[mask];
  unordered_set<int> s;
  for (int i = 0; mask >> i; i++)
    s.insert(grundy(mask >> i + 1 | (mask & (1 << i) - 1)));
  int mex = 0;
  while (s.count(mex)) mex++;
  return game[mask] = mex;
}
int main() {
  int n;
  cin >> n;
  while (n--) {
    int x;
    cin >> x;
    for (int i = 2; i * i <= x; i++)
      if (x % i == 0) {
        int cnt = -1;
        while (x % i == 0) x /= i, cnt++;
        mask[i] |= 1 << cnt;
      }
    if (x > 1) mask[x] |= 1;
  }
  int ans = 0;
  for (auto x : mask) ans ^= grundy(x.second);
  cout << (ans ? "Mojtaba" : "Arpa");
}
