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_N = 110;
int a[max_N];
map<int, int> spgn;
int find_grundy(int x);
int main() {
  spgn[0] = -1;
  spgn[1] = 0;
  int N;
  cin >> N;
  for (int i = 1; i <= N; ++i) {
    cin >> a[i];
  }
  map<int, int> primes;
  for (int i = 1; i <= N; ++i) {
    int R = sqrt(a[i]);
    int x = a[i];
    for (int j = 2; j <= R; ++j) {
      int pwr = 0;
      while (x % j == 0) {
        x /= j;
        ++pwr;
      }
      if (pwr > 0) {
        primes[j] |= (1 << pwr);
      }
    }
    if (x > 1) {
      primes[x] |= 2;
    }
  }
  int gn = 0;
  for (auto &p : primes) {
    gn ^= find_grundy(p.second);
  }
  if (gn == 0) {
    cout << "arpa" << endl;
  } else {
    cout << "mojtaba" << endl;
  }
}
int find_grundy(int x) {
  if (spgn.find(x) == spgn.end()) {
    set<int> reach;
    for (int k = 1; (x >> k) > 0; ++k) {
      int y = (x >> k) | (((1 << k) - 1) & x);
      reach.insert(find_grundy(y));
    }
    for (int i = 0; i < 35; ++i) {
      if (reach.find(i) == reach.end()) {
        spgn[x] = i;
        break;
      }
    }
  }
  return spgn[x];
}
