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 inf = 0x3f3f3f3f;
const int maxn = 100000;
map<int, int> H;
int SG(int mask) {
  if (H.find(mask) != H.end()) {
    return H[mask];
  }
  set<int> p;
  for (int i = 1; i <= 30; i++) {
    if ((mask >> i) | (mask & ((1 << (i - 1)) - 1)) != mask)
      p.insert(SG((mask >> i) | (mask & ((1 << (i - 1)) - 1))));
  }
  int res = 0;
  while (p.find(res) != p.end()) res++;
  return H[mask] = res;
}
int a[maxn];
int n;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(nullptr);
  cin >> n;
  H[0] = 0;
  map<int, int> game;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (int i = 0; i < n; i++) {
    for (int j = 2; j * j <= a[i]; j++) {
      int tmp = 0;
      while (a[i] % j == 0) {
        tmp++;
        a[i] /= j;
      }
      if (tmp) {
        game[j] |= 1 << (tmp - 1);
      }
    }
    if (a[i] != 1) {
      game[a[i]] |= 1;
    }
  }
  int xsum = 0;
  for (auto p : game) {
    xsum ^= SG(p.second);
  }
  if (!xsum) {
    cout << "Arpa" << endl;
  } else {
    cout << "Mojtaba" << endl;
  }
}
