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 long long MOD = 1000000007;
const int INF = 1e9;
const long long LINF = 1e16;
const double PI = acos(-1.0);
int dx[8] = {0, 0, 1, -1, 1, 1, -1, -1};
int dy[8] = {1, -1, 0, 0, 1, -1, 1, -1};
long long N;
long long ans = 0LL;
template <size_t sz>
struct bitset_comparer {
  bool operator()(const bitset<sz> &b1, const bitset<sz> &b2) const {
    return b1.to_ulong() < b2.to_ulong();
  }
};
map<int, bitset<35>> ma;
map<bitset<35>, int, bitset_comparer<35>> memo;
int game(bitset<35> b) {
  if (memo[b]) return memo[b];
  if (b.count() == 0) return 0;
  int m = 0;
  for (long long(i) = (0); (i) < (35); (i)++) {
    if (b[i]) m = i;
  }
  set<int> se;
  for (long long(i) = (1); (i) < (m + 1); (i)++) {
    bitset<35> c(b);
    c[i] = 0;
    for (long long(j) = (i + 1); (j) < (35); (j)++) {
      if (c[j]) {
        c[j] = 0;
        c[j - i] = 1;
      }
    }
    se.insert(game(c));
  }
  int subg = 0;
  while (se.count(subg)) subg++;
  return memo[b] = subg;
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  cin >> N;
  for (long long(i) = (0); (i) < (N); (i)++) {
    int a;
    cin >> a;
    for (int p = 2; p * p <= a; p++) {
      int cnt = 0;
      while (a % p == 0) {
        cnt++;
        a /= p;
      }
      ma[p][cnt] = 1;
    }
    if (a > 1) ma[a][1] = 1;
  }
  int grundy = 0;
  for (auto itr : ma) {
    grundy ^= game(itr.second);
  }
  cout << ((grundy != 0) ? "Mojtaba" : "Arpa") << endl;
  return 0;
}
