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;
bool prime[10000];
map<int, int> tmpp;
int o = 0;
map<int, vector<int> > factors;
map<int, int> gr;
int power(int x, int y) {
  int ret = 1;
  for (int i = 0; i < y; i++) ret *= x;
  return ret;
}
int grundy(int mask) {
  if (mask <= 1) return 0;
  if (gr.count(mask)) return gr[mask];
  set<int> my;
  for (int i = 1; i < 31; i++) {
    int newMask = 0;
    bool ok = false;
    for (int k = i; k < 31; k++) {
      if (mask & (1 << k)) ok = true;
    }
    if (ok) {
      for (int k = 1; k < 31; k++) {
        if (k < i)
          newMask |= (mask & (1 << k));
        else {
          if (mask & (1 << k)) newMask |= 1 << (k - i);
        }
      }
      my.insert(grundy(newMask));
    }
  }
  int ret = 0;
  set<int>::iterator it = my.begin();
  while (it != my.end() && *it == ret) ret++, it++;
  return gr[mask] = ret;
}
int n;
int main() {
  cin >> n;
  vector<int> v;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    v.push_back(x);
    int tmp = x;
    for (long long j = 2; j * j <= tmp; j++) {
      int cnt = 0;
      while (tmp % j == 0) cnt++, tmp /= j;
      if (cnt) {
        factors[j].push_back(cnt);
      }
    }
    if (tmp != 1) {
      factors[tmp].push_back(1);
    }
  }
  int ans = 0;
  for (map<int, vector<int> >::iterator it = factors.begin();
       it != factors.end(); it++) {
    vector<int> vv = it->second;
    int mask = 0;
    for (int i = 0; i < (int)vv.size(); i++) {
      mask |= (1 << vv[i]);
    }
    int res = grundy(mask);
    ans ^= res;
  }
  if (ans == 0)
    cout << "Arpa\n";
  else
    cout << "Mojtaba\n";
  return 0;
}
