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;
struct pat {
  int x, y;
  pat(int x = 0, int y = 0) : x(x), y(y) {}
  bool operator<(const pat &p) const { return x == p.x ? y < p.y : x < p.x; }
};
template <typename TP>
inline void read(TP &tar) {
  TP ret = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    ret = ret * 10 + (ch - '0');
    ch = getchar();
  }
  tar = ret * f;
}
template <typename TP, typename... Args>
inline void read(TP &t, Args &...args) {
  read(t), read(args...);
}
namespace RKK {
int n, ans;
map<int, int> pr;
map<int, int> sg;
int calc(int s) {
  if (sg.find(s) != sg.end()) return sg[s];
  if (!s) return sg[s] = 0;
  set<int> se;
  for (int b = 1; b <= 30; b++)
    if (s >> b) se.insert(calc((s & ((1 << b) - 1)) | (s >> b)));
  int ret = 0;
  while (se.find(ret) != se.end()) ret++;
  return sg[s] = ret;
}
int main() {
  read(n);
  for (int i = 1, x; i <= n; i++) {
    read(x);
    for (int j = 2; j * j <= x; j++)
      if (x % j == 0) {
        int c = 0;
        while (x % j == 0) x /= j, c++;
        pr[j] |= (1 << c);
      }
    if (x != 1) pr[x] |= (1 << 1);
  }
  for (auto it = pr.begin(); it != pr.end(); ++it) ans ^= calc(it->second);
  puts(ans ? "moJtaBa" : "aRPa");
  return 0;
}
}  // namespace RKK
int main() { return RKK::main(); }
