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> mask;
unordered_map<int, int> dp, was;
void load() {
  scanf("%d", &N);
  while (N--) {
    int x;
    scanf("%d", &x);
    for (int i = 2; i * i <= x; i++) {
      if (x % i) continue;
      int tmp = 0;
      for (; !(x % i); x /= i) tmp++;
      mask[i] |= 1 << tmp - 1;
    }
    if (x > 1) mask[x] |= 1;
  }
}
int grundy(int mask) {
  int &ref = dp[mask];
  if (was[mask]) return ref;
  was[mask] = 1;
  vector<int> pos;
  for (int i = 0; i < 30; i++)
    if (mask >> i & 1) pos.push_back(i + 1);
  bool bio[35] = {0};
  for (int i = 1; i <= 30; i++) {
    int curr = mask;
    for (auto it : pos)
      if (it >= i) curr ^= 1 << it - 1;
    for (auto it : pos)
      if (it > i) curr |= 1 << it - i - 1;
    if (curr != mask) bio[grundy(curr)] = true;
  }
  for (ref = 0; bio[ref]; ref++)
    ;
  return ref;
}
int solve() {
  dp[0] = 0;
  was[0] = 1;
  int sol = 0;
  for (auto it : mask) sol ^= grundy(it.second);
  return sol;
}
int main() {
  load();
  puts(solve() ? "Mojtaba" : "Arpa");
  return 0;
}
