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;
map<long long, long long> dp;
map<long long, long long> mapi;
long long grundy(long long val) {
  if (val == 1) {
    return 0;
  }
  set<long long> seti;
  seti.clear();
  long long haha, papa;
  if (dp.find(val) != dp.end()) {
    return dp[val];
  }
  long long i = 1;
  while (val >= (1LL << i)) {
    haha = val % (1LL << i);
    papa = val / (1LL << i);
    seti.insert(grundy(haha | papa));
    i++;
  }
  for (i = 0; i < 10000; i++) {
    if (seti.find(i) == seti.end()) {
      dp[val] = i;
      return i;
    }
  }
}
vector<vector<long long> > vec(123);
long long factorise(long long ind, long long val) {
  long long i;
  for (i = 2; i * i <= val; i++) {
    while (val % i == 0) {
      val /= i;
      vec[ind].push_back(i);
      mapi[i] = 0;
    }
  }
  if (val != 1) {
    mapi[val] = 0;
    vec[ind].push_back(val);
  }
  return 0;
}
long long a[123];
long long lol[123456];
int main() {
  std::ios::sync_with_stdio(false);
  long long n;
  cin >> n;
  long long i;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (i = 0; i < n; i++) {
    factorise(i, a[i]);
  }
  long long coutner = 1;
  map<long long, long long>::iterator it;
  for (it = mapi.begin(); it != mapi.end(); it++) {
    it->second = coutner++;
  }
  long long prev, counti, j;
  for (i = 0; i < n; i++) {
    if (vec[i].empty()) continue;
    sort(vec[i].begin(), vec[i].end());
    prev = vec[i][0];
    counti = 1;
    for (j = 1; j < vec[i].size(); j++) {
      if (vec[i][j] != prev) {
        lol[mapi[prev]] |= (1LL << counti);
        prev = vec[i][j];
        counti = 1;
      } else {
        counti++;
      }
    }
    lol[mapi[prev]] |= (1LL << counti);
  }
  long long ans = 0;
  for (i = 1; i < coutner; i++) {
    ans ^= grundy(lol[i]);
  }
  if (!ans) {
    cout << "Arpa" << endl;
  } else {
    cout << "Mojtaba" << endl;
  }
  return 0;
}
