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 long long MOD = 1e9 + 7;
map<int, int> memo;
int value(int n) {
  if (n == 1) return 0;
  if (memo.find(n) != memo.end()) return memo[n];
  set<int> s;
  for (int i = 1; i < 30; i++) {
    int m = n & ((1 << i) - 1);
    for (int j = i; j <= 31; j++) {
      if (n & (1 << j)) m |= (1 << (j - i));
    }
    if (m == n) break;
    s.insert(value(m));
  }
  for (int i = 0;; i++) {
    if (s.find(i) == s.end()) return memo[n] = i;
  }
}
int pdp[40000];
vector<int> primes;
void sieve() {
  for (int i = 2; i < 40000; i++) {
    if (pdp[i]) continue;
    primes.push_back(i);
    for (int j = i; j < 40000; j += i) {
      pdp[j] = 1;
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  sieve();
  int N;
  cin >> N;
  map<int, int> games;
  for (int i = 0; i < N; i++) {
    int x;
    cin >> x;
    for (int p : primes) {
      if (x % p) continue;
      int k = 0;
      while (x % p == 0) x /= p, k++;
      games[p] |= (1 << k);
    }
    if (x > 1) games[x] |= (1 << 1);
  }
  int total = 0;
  for (auto& g : games) {
    total ^= value(g.second);
  }
  cout << (total ? "Mojtaba" : "Arpa") << '\n';
  return 0;
}
