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 MAX = 1e2 + 6;
map<set<int>, int> memo;
int arr[MAX];
int n;
int mex(vector<int> v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
  for (int i = int(0); i < int(v.size()); i++) {
    if (v[i] != i) {
      return i;
    }
  }
  return v.size();
}
int roll(set<int> state) {
  if (state.empty()) {
    return 0;
  }
  if (memo.count(state)) {
    return memo[state];
  }
  int &ans = memo[state];
  int maxx = *state.rbegin();
  ans = 0;
  vector<int> states;
  for (int i = int(1); i < int(maxx + 1); i++) {
    vector<int> new_vals;
    for (auto &each : state) {
      if (each < i) {
        new_vals.push_back(each);
      } else if (each > i) {
        new_vals.push_back(each - i);
      }
    }
    set<int> new_state(new_vals.begin(), new_vals.end());
    states.push_back(roll(new_state));
  }
  ans = mex(states);
  return ans;
}
int main() {
  scanf("%d", &n);
  map<int, set<int> > mp;
  for (int i = int(1); i < int(n + 1); i++) {
    scanf("%d", arr + i);
    set<int> cur;
    for (long long j = 2; j * j <= arr[i]; j++) {
      int e = 0;
      while (arr[i] % j == 0) {
        arr[i] /= j;
        e++;
      }
      if (e) {
        mp[j].insert(e);
      }
    }
    if (arr[i] != 1) {
      mp[arr[i]].insert(1);
    }
  }
  int x = 0;
  for (auto &each : mp) {
    x ^= roll(each.second);
  }
  puts(x ? "Mojtaba" : "Arpa");
  return 0;
}
