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;
int n, a[101];
bool notp[100010];
vector<int> prime;
map<int, int> qmask;
int sg[1 << 15];
map<int, int> big_sg;
int search(int x) {
  if (x < (1 << 15)) return sg[x];
  if (big_sg.find(x) != big_sg.end()) return big_sg[x];
  vector<bool> vis(40);
  for (int j = 0; j < 31 && (1 << j) <= x; j++) {
    int small_all_one = (1 << j) - 1;
    int big_all_one = ~small_all_one;
    bool valid = false;
    valid = (big_all_one & x) > 0;
    int new_mask = (x & small_all_one) | ((x & big_all_one) >> (j + 1));
    if (valid) {
      int next_sg = search(new_mask);
      if (next_sg > 39) next_sg = 39;
      vis[next_sg] = true;
    }
  }
  for (int aa = 0; aa < 40; aa++)
    if (!vis[aa]) {
      big_sg[x] = aa;
      break;
    }
  return big_sg[x];
}
int main() {
  sg[0] = 0;
  for (int i = 1; i < (1 << 15); i++) {
    vector<bool> vis(40);
    for (int j = 0; j < 15 && (1 << j) <= i; j++) {
      int small_all_one = (1 << j) - 1;
      int big_all_one = ~small_all_one;
      bool valid = false;
      valid = (big_all_one & i) > 0;
      int new_mask = (i & small_all_one) | ((i & big_all_one) >> (j + 1));
      if (valid) vis[sg[new_mask]] = true;
    }
    for (int aa = 0; aa < 30; aa++)
      if (!vis[aa]) {
        sg[i] = aa;
        break;
      }
  }
  notp[1] = true;
  for (int i = 2; i <= 100000; i++) {
    if (notp[i]) continue;
    prime.push_back(i);
    for (int j = i + i; j <= 100000; j += i) notp[j] = true;
  }
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    for (auto p : prime) {
      int qq = 0;
      while (a[i] % p == 0) {
        a[i] /= p;
        qq++;
      }
      if (qq > 0) {
        qmask[p] |= 1 << (qq - 1);
      }
    }
    if (a[i] > 1) qmask[a[i]] |= 1;
  }
  int ans = 0;
  for (auto pair_p_qqmask : qmask) {
    ans ^= search(pair_p_qqmask.second);
  }
  if (ans == 0)
    puts("Arpa");
  else
    puts("Mojtaba");
}
