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;
template <typename T, typename C>
ostream &operator<<(ostream &os, pair<T, C> x) {
  return os << "<" << x.first << ", " << x.second << ">";
}
template <typename T>
auto operator<<(ostream &os, T x) ->
    typename enable_if<is_same<decltype(x.begin()), decltype(x.end())>::value &&
                           !is_same<T, string>::value,
                       ostream &>::type {
  os << "{";
  int cou = 0;
  for (auto c : x) {
    if (cou++) os << ", ";
    os << c;
  }
  return os << "}";
}
template <typename T>
string strmask(T r) {
  string ans;
  for (int i = 0; i < (8 * (int)sizeof(T)); i++) {
    ans += '0' + !!(((T)1 << i) & r);
    if (i % 5 == 4) ans += '.';
  }
  return ans;
}
const int MB = 30;
unordered_map<bitset<MB>, int> memo;
int nimber(bitset<MB> x) {
  if (memo.count(x)) return memo[x];
  bitset<MB> seen;
  int last = 0;
  for (int i = 0; i < (MB); i++)
    if (x[i]) last = i;
  for (int l = 1; l <= (last); l++) {
    auto y = x;
    for (int i = l; i <= (MB - 1); i++)
      if (y[i]) {
        y[i] = false;
        y[i - l] = true;
      }
    if (0)
      cout << "last"
           << " = " << (last) << ' ' << "make " << y << "from " << x << endl;
    seen[nimber(y)] = true;
  }
  for (int i = 0; i < (MB); i++)
    if (!seen[i]) {
      memo[x] = i;
      if (0) cout << "nimber " << x << " = " << i << endl;
      return i;
    }
  assert(false);
}
int main() {
  map<int, bitset<MB> > state;
  int n;
  scanf("%d", &n);
  for (int i = 0; i < (n); i++) {
    int x;
    scanf("%d", &x);
    for (int p = 2; p * p <= x; ++p) {
      if (x % p == 0) {
        int e = 0;
        while (x % p == 0) {
          x /= p;
          e++;
        }
        state[p][e] = true;
      }
    }
    if (x > 1) state[x][1] = true;
  }
  int ans = 0;
  for (auto &c : state) ans ^= nimber(c.second);
  if (ans)
    printf("Mojtaba");
  else
    printf("Arpa");
}
