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;
int n;
vector<vector<int> > v;
map<int, int> mp;
map<vector<int>, int> dp;
vector<int> val;
int calc(vector<int> &val) {
  sort(val.begin(), val.end());
  val.resize(unique(val.begin(), val.end()) - val.begin());
  if (val.empty()) return 0;
  auto it = dp.insert({val, -1}).first;
  int &ret = it->second;
  if (ret != -1) return ret;
  ret = 0;
  set<int> g;
  vector<int> nval;
  for (int take = 1; take <= val.back(); ++take) {
    nval.clear();
    for (int i = 0; i < val.size(); ++i)
      if (val[i] > take)
        nval.push_back(val[i] - take);
      else if (val[i] < take)
        nval.push_back(val[i]);
    g.insert(calc(nval));
  }
  while (g.find(ret) != g.end()) ++ret;
  return ret;
}
int main() {
  scanf("%d", &n);
  for (int i = 0, x; i < n; ++i) {
    scanf("%d", &x);
    for (int i = 2; i * i <= x; ++i) {
      if (x % i == 0) {
        int p = 0;
        while (x % i == 0) {
          ++p;
          x /= i;
        }
        if (mp.find(i) == mp.end()) {
          mp[i] = v.size();
          v.push_back(vector<int>());
        }
        v[mp[i]].push_back(p);
      }
    }
    if (x != 1) {
      swap(x, i);
      if (mp.find(i) == mp.end()) {
        mp[i] = v.size();
        v.push_back(vector<int>());
      }
      v[mp[i]].push_back(1);
      swap(x, i);
    }
  }
  if (v.empty()) {
    puts("Arpa");
    return 0;
  }
  int res = 0;
  for (int i = 0; i < v.size(); ++i) {
    val = v[i];
    res ^= calc(val);
  }
  if (res)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
