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>
std::map<int, int> map;
std::map<int, int> sg;
int calc(int mask) {
  if (mask == 0) return 0;
  if (sg.find(mask) != sg.end()) return sg[mask];
  std::set<int> set;
  for (int i = 0; (1 << i) <= mask; ++i) {
    set.emplace(calc((mask >> i + 1) | (mask & (1 << i) - 1)));
  }
  int x = 0;
  while (set.count(x)) ++x;
  return sg[mask] = x;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    int x;
    scanf("%d", &x);
    for (int p = 2; p * p <= x; ++p) {
      if (x % p == 0) {
        int c = 0;
        while (x % p == 0) x /= p, ++c;
        map[p] |= 1 << c - 1;
      }
    }
    if (x > 1) map[x] |= 1 << 0;
  }
  int result = 0;
  for (auto t : map) {
    int all = t.second;
    result ^= calc(all);
  }
  puts(result ? "Mojtaba" : "Arpa");
}
