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;
map<int, int> primes;
void get(int p, int e) { primes[p] |= (1 << e); }
void getPrimes(int n) {
  for (int p = 2; p * p <= n; ++p) {
    if (n % p == 0) {
      int e = 0;
      while (n % p == 0) {
        n /= p;
        ++e;
      }
      get(p, e);
    }
  }
  if (n > 1) get(n, 1);
  return;
}
int mex(set<int> G) {
  int m = 0;
  for (int g : G) {
    if (m == g)
      ++m;
    else
      return m;
  }
  return m;
}
map<int, int> dp;
int grundy(int mask) {
  if (mask == 1) {
    return 0;
  } else if (dp.count(mask)) {
    return dp[mask];
  } else {
    set<int> G;
    int pref = mask & 1;
    int pot = 0;
    while (pref < mask) {
      int new_mask = pref | (mask >> (pot + 1));
      int e = (mask >> (pot + 1)) & 1;
      if (e > 0) pref ^= (1 << (pot + 1));
      G.insert(grundy(new_mask));
      ++pot;
    }
    return dp[mask] = mex(G);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    getPrimes(a);
  }
  int ans = 0;
  for (auto [p, mask] : primes) {
    ans ^= grundy(mask);
  }
  cout << (ans != 0 ? "Mojtaba" : "Arpa") << '\n';
  return 0;
}
