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 N = 30;
map<int, int> dp;
int sg(int mask) {
  if (mask == 0) return 0;
  if (dp.count(mask)) return dp[mask];
  vector<bool> next(N);
  for (int i = 1; i < N; i++) {
    int left = mask & ((1 << (i - 1)) - 1);
    int right = mask >> i;
    if (mask == left) continue;
    int next_mask = left | right;
    next[sg(next_mask)] = true;
  }
  for (int i = 0; i < N; i++) {
    if (next[i] == false) {
      return dp[mask] = i;
    }
  }
  assert(0);
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  map<int, vector<int>> primes;
  for (int i = 0; i < n; i++) {
    for (int j = 2; j * j <= a[i]; j++) {
      int num = 0;
      while (a[i] % j == 0) {
        a[i] /= j;
        num++;
      }
      if (num > 0) primes[j].push_back(num);
    }
    if (a[i] != 1) primes[a[i]].push_back(1);
  }
  int x = 0, mask;
  for (auto p : primes) {
    mask = 0;
    for (auto i : p.second) {
      mask |= (1 << (i - 1));
    }
    x ^= sg(mask);
  }
  cout << (x == 0 ? "Arpa" : "Mojtaba") << '\n';
  return 0;
}
