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;
istream& in = cin;
int n, a[110];
bool vis[(31800)];
vector<int> prime;
void Init() {
  for (int i = 2; i < (31800); ++i) {
    if (!vis[i]) {
      prime.push_back(i);
      for (int j = i + i; j < (31800); j += i) {
        vis[j] = 1;
      }
    }
  }
}
void input() {
  in >> n;
  for (int i = 1; i <= n; ++i) in >> a[i];
}
unordered_map<int, vector<int>*> mmp;
void put(int p, int num) {
  if (!mmp.count(p)) {
    mmp[p] = new vector<int>();
  }
  mmp[p]->push_back(num);
}
unordered_map<int, int> SG;
int dfs(int k) {
  if (k == 0) return 0;
  if (SG.count(k)) return SG[k];
  set<int> si;
  int hbit;
  for (int i = 30; i >= 0; --i) {
    if (k & (1 << i)) {
      hbit = i;
      break;
    }
  }
  vector<int> dig;
  for (int i = 0; i < 31; ++i) {
    if (k & (1 << i)) {
      dig.push_back(i);
    }
  }
  for (int i = 1; i <= hbit; ++i) {
    int g = 0;
    for (int d : dig) {
      if (d > i) {
        g |= (1 << (d - i));
      } else if (d < i) {
        g |= (1 << d);
      }
    }
    si.insert(dfs(g));
  }
  int sg = 0;
  while (si.count(sg)) sg++;
  return SG[k] = sg;
}
int main() {
  int TEST_CASE = 1;
  while (TEST_CASE-- > 0) {
    input();
    Init();
    for (int i = 1; i <= n; ++i) {
      int p = a[i];
      for (int div : prime) {
        int num = 0;
        while (p % div == 0) {
          num++;
          p /= div;
        }
        if (num) {
          put(div, num);
        }
      }
      if (p != 1) {
        put(p, 1);
      }
    }
    unordered_map<int, vector<int>*>::iterator it = mmp.begin();
    int ans = 0;
    while (it != mmp.end()) {
      vector<int>& tmp = *(it->second);
      int key = 0;
      for (int t : tmp) {
        key |= (1 << t);
      }
      ans ^= dfs(key);
      it++;
    }
    if (ans) {
      cout << "Mojtaba" << endl;
    } else {
      cout << "Arpa" << endl;
    }
  }
  return 0;
}
