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;
map<int, int> pphav;
int p2(int a) { return 1 << a; }
void fac(int a) {
  for (int i = 2; i * i <= a; ++i) {
    if (a % i == 0) {
      int cp = i;
      int pw = 0;
      while (a % i == 0) {
        a /= i;
        ++pw;
      }
      pphav[cp] |= p2(pw);
    }
  }
  if (a != 1) pphav[a] |= p2(1);
}
map<int, int> g;
const int mpw = 29;
int allbit = p2(mpw + 1) - 1;
int grund(int msk) {
  if (msk & 1) msk ^= 1;
  if (g.find(msk) != g.end()) return g[msk];
  vector<int> sn(33);
  for (int i = 1; (msk & (allbit ^ (p2(i) - 1))) != 0; ++i) {
    sn[grund((msk & (p2(i) - 1)) | (msk >> i))] = 1;
  }
  int r = 0;
  while (sn[r]) ++r;
  return g[msk] = r;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int z = 0; z < (n); ++z) {
    int a;
    cin >> a;
    fac(a);
  }
  int totgrund = 0;
  for (auto i = (pphav).begin(); i != (pphav).end(); ++i)
    totgrund ^= grund(i->second);
  if (totgrund)
    cout << "Mojtaba" << endl;
  else
    cout << "Arpa" << endl;
  return 0;
}
