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;
map<int, int> id;
int pri[5050];
int tot;
int zt[5050];
void pia(int x) {
  int c, p;
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) {
      c = 0;
      while (x % i == 0) c++, x /= i;
      p = id[i];
      if (p)
        zt[p] |= (1 << (c - 1));
      else {
        id[i] = ++tot;
        pri[tot] = i;
        zt[tot] |= (1 << (c - 1));
      }
    }
  if (x == 1) return;
  p = id[x];
  if (p)
    zt[p] |= 1;
  else {
    id[x] = ++tot;
    pri[tot] = x;
    zt[tot] |= 1;
  }
}
map<int, int> sg;
map<int, bool> did;
int dfs(int cur) {
  if (!cur) return 0;
  if (did[cur]) return sg[cur];
  bool book[33];
  memset(book, 0, sizeof(book));
  int nxt;
  for (int i = 0; cur >> i; ++i) {
    nxt = ((cur >> (i + 1)) | (cur & ((1 << i) - 1)));
    book[dfs(nxt)] = 1;
  }
  for (int i = 0;; ++i)
    if (!book[i]) {
      sg[cur] = i;
      did[cur] = 1;
      return i;
    }
}
int main() {
  scanf("%d", &n);
  int xx;
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &xx);
    pia(xx);
  }
  int ans = 0;
  for (int i = 1; i <= tot; ++i) ans ^= dfs(zt[i]);
  puts(ans ? "Mojtaba" : "Arpa");
  return 0;
}
