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;
inline void out(int a) { printf("%d\n", a); }
inline void out(int a, int b) { printf("%d %d\n", a, b); }
inline void outf(double a) { printf("%3.lf\n", a); }
inline void outf(double a, double b) { printf("%3.lf %3.lf\n", a, b); }
inline void base() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
}
map<int, int> mask, dp, mark;
int dua[32];
int mv(int mask, int k) { return (mask >> k) | (mask & ((1 << k) - 1)); }
int get(int mask) {
  if (mask == 0) return 0;
  if (dp.count(mask)) return dp[mask];
  int mxbit = 32 - __builtin_clz(mask);
  vector<int> tmp;
  for (int i = 1; i < mxbit; i++)
    if (mv(mask, i) != mask) tmp.push_back(get(mv(mask, i)));
  for (int i = 0; i < tmp.size(); i++) mark[tmp[i]] = mask;
  while (mark[dp[mask]] == mask) dp[mask]++;
  return dp[mask];
}
int main() {
  base();
  dua[0] = 1;
  for (int(i) = (1); (i) <= (31); (i)++) dua[i] = dua[i - 1] * 2;
  int n;
  cin >> n;
  for (int(i) = 0; (i) < (n); (i)++) {
    int a;
    cin >> a;
    for (int j = 2; j * j <= a; j++) {
      if (a % j == 0) {
        int cnt = 0;
        mask[j] |= 1;
        while (a % j == 0) {
          cnt++;
          a /= j;
        }
        mask[j] |= dua[cnt];
      }
    }
    if (a != 1) mask[a] |= 3;
  }
  int ans = 0;
  for (map<int, int>::iterator i = mask.begin(); i != mask.end(); i++) {
    ans ^= get(i->second);
  }
  if (ans)
    cout << "Mojtaba" << endl;
  else
    cout << "Arpa" << endl;
  return 0;
}
