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;
void smain();
int main() {
  ios_base::sync_with_stdio(0);
  smain();
  return 0;
}
int n, a[101];
vector<pair<int, int> > fact(int x) {
  vector<pair<int, int> > res;
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) {
      int c = 0;
      for (; x % i == 0; x /= i) c += 1;
      res.emplace_back(i, c);
    }
  if (x != 1) res.emplace_back(x, 1);
  return res;
}
map<vector<int>, int> sg;
int calc(vector<int> x) {
  sort(x.rbegin(), x.rend());
  x.resize(unique(x.begin(), x.end()) - x.begin());
  while (!x.empty() && x.back() == 0) x.pop_back();
  if (x.empty()) return 0;
  if (sg.count(x)) return sg.at(x);
  set<int> v;
  int mx = x.front();
  for (int i = 1; i <= mx; ++i) {
    vector<int> y = x;
    for (auto &j : y) {
      if (j >= i)
        j -= i;
      else
        break;
    }
    v.insert(calc(y));
  }
  int res = 0;
  while (v.count(res)) res += 1;
  sg.emplace(x, res);
  return res;
}
int solve() {
  map<int, vector<int> > g;
  for (int i = 0; i < n; i++) {
    auto t = fact(a[i]);
    for (auto it : t) g[it.first].push_back(it.second);
  }
  int r = 0;
  for (auto it : g) r ^= calc(it.second);
  return r;
}
void smain() {
  for (; cin >> n;) {
    for (int i = 0; i < n; i++) cin >> a[i];
    int r = solve();
    cout << (r == 0 ? "Arpa" : "Mojtaba") << endl;
  }
}
