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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const long double PI = 3.14159265358979323846;
const long double eps = 1e-5;
const int INF = numeric_limits<int>::max();
const long long LINF = numeric_limits<long long>::max();
const long long mod = 1000 * 1000 * 1000 + 7;
vector<int> genPrimes(int N) {
  vector<int> p(N + 1, 1);
  vector<int> res;
  for (int i = 2; i < p.size(); ++i) {
    if (p[i]) {
      res.push_back(i);
      for (int j = i + i; j < p.size(); j += i) p[j] = 0;
    }
  }
  return res;
}
map<int, int> mem;
int get(int n) {
  if (n == 0) return 0;
  if (mem.find(n) != mem.end()) return mem[n];
  vector<int> forb;
  for (int i = 1;; ++i) {
    int a = n >> i;
    int b = n & ((1 << (i - 1)) - 1);
    int x = a | b;
    forb.push_back(get(x));
    if (a == 0) break;
  }
  sort(forb.begin(), forb.end());
  if ((forb.empty()) || (forb[0] != 0)) return mem[n] = 0;
  for (int i = 1; i < forb.size(); ++i) {
    if (forb[i] > forb[i - 1] + 1) return mem[n] = forb[i - 1] + 1;
  }
  return mem[n] = forb.back() + 1;
}
void solve() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  vector<int> primes = genPrimes(40000);
  map<int, int> degr;
  for (int i = 0; i < n; ++i) {
    int x = a[i];
    for (int j = 0; j < primes.size(); ++j) {
      if ((x % primes[j]) == 0) {
        int c = 0;
        while ((x % primes[j]) == 0) {
          ++c;
          x /= primes[j];
        }
        if (degr.find(primes[j]) == degr.end()) degr[primes[j]] = 0;
        degr[primes[j]] |= (1 << (c - 1));
      }
    }
    if (x != 1) {
      if (degr.find(x) == degr.end()) degr[x] |= 1;
    }
  }
  int res = 0;
  for (auto e : degr) {
    res ^= get(e.second);
  }
  if (res == 0)
    cout << "Arpa" << endl;
  else
    cout << "Mojtaba" << endl;
}
int main() {
  solve();
  return 0;
}
