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> mp;
map<int, int> sg;
int t[30005], cnt = 0;
int cal(int p) {
  if (sg.find(p) != sg.end()) return sg[p];
  bool vis[45];
  int i;
  memset(vis, 0, sizeof(vis));
  for (i = 31; i >= 1; i--) {
    if ((p & (1 << i))) {
      break;
    }
  }
  for (; i >= 1; i--) {
    int to = ((p >> i) | (p & ((1 << i) - 1)));
    vis[cal(to)] = 1;
  }
  sg[p] = 0;
  while (vis[sg[p]]) sg[p]++;
  return sg[p];
}
int main() {
  int i, n, num, x;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &x);
    num = 2;
    while (num * num <= x) {
      if (x % num == 0) {
        int p = 0;
        while (x % num == 0) {
          x /= num;
          p++;
        }
        if (mp.find(num) == mp.end()) {
          cnt++;
          mp[num] = cnt;
        }
        int pos = mp[num];
        t[pos] |= (1 << p);
      }
      num++;
    }
    if (x > 1) {
      if (mp.find(x) == mp.end()) {
        cnt++;
        mp[x] = cnt;
      }
      int pos = mp[x];
      t[pos] |= 2;
    }
  }
  int q = 0;
  for (i = 1; i <= cnt; i++) {
    q ^= cal(t[i]);
  }
  if (q) {
    puts("Mojtaba");
  } else {
    puts("Arpa");
  }
  return 0;
}
