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 = 1e9, M = 1e5 + 1, INF = 1e5, mod = 1e9 + 7;
const double PI = 3.141592653589793238462643383279502884197, eps = 1e-15;
int is[M];
vector<int> prms;
map<int, int> dp;
void seive() {
  for (long long i = 2; i * i <= N; i++) {
    if (!is[i]) {
      prms.push_back(i);
      for (long long j = i * i; j * j <= N; j += i) is[j] = 1;
    }
  }
}
int solve(int mask) {
  bool arr[100] = {0};
  int x = 0;
  mask &= ~1;
  int &ret = dp[mask];
  if (ret) return ret - 1;
  for (int i = 1; x < mask; i++) {
    arr[solve((mask >> i) | x)] = 1;
    x |= (mask & (1 << i));
  }
  for (int i = 0; i < 40; i++)
    if (!arr[i]) {
      ret = i + 1;
      break;
    }
  return ret - 1;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, ans = 0, cnt;
  set<int> nums;
  cin >> n;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  seive();
  int masks[M] = {0};
  for (int i = 0; i < n; i++) {
    for (unsigned int j = 0; j < prms.size() && prms[j] <= a[i]; j++) {
      cnt = 0;
      while (a[i] % prms[j] == 0) {
        cnt++;
        a[i] /= prms[j];
      }
      masks[j] |= (1 << cnt);
    }
    if (a[i] > 1) nums.insert(a[i]);
  }
  for (unsigned int i = 0; i < prms.size(); i++) {
    dp.clear();
    ans ^= solve(masks[i]);
  }
  cout << (ans ^ (nums.size() % 2) ? "Mojtaba" : "Arpa");
  return 0;
}
