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;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
map<int, int> mp;
int f(int mask) {
  if (mp.count(mask)) return mp[mask];
  if (mask <= 1) return mp[mask] = 0;
  set<int> grundy;
  for (int i = 1; i < 31; i++) {
    int newmask = 0;
    for (int j = 1; j < 31; j++) {
      if (!(mask & (1 << j))) continue;
      if (j < i)
        newmask |= (1 << j);
      else if (j > i)
        newmask |= (1 << (j - i));
    }
    if (newmask == mask) continue;
    assert(newmask < mask);
    grundy.insert(f(newmask));
  }
  int val = 0;
  for (auto it : grundy) {
    if (it != val) break;
    val++;
  }
  return mp[mask] = val;
}
map<int, int> cnt;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    for (int i = 2; i * i <= x; ++i) {
      int v = 0;
      while (x % i == 0) {
        x = x / i;
        v++;
      }
      if (!v) continue;
      cnt[i] |= (1 << v);
    }
    if (x > 1) cnt[x] |= (1 << 1);
  }
  int ans = 0;
  for (auto x : cnt) {
    ans ^= f(x.second);
  }
  puts(ans ? "Mojtaba" : "Arpa");
  return 0;
}
