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> sg, res;
int n, a[104];
int Prime(int x) {
  for (int i = 2; i <= sqrt(x); i++) {
    int cnt = 0;
    while (x % i == 0) {
      x /= i;
      cnt++;
    }
    if (cnt) sg[i] |= (1 << (cnt - 1));
  }
  if (x > 1) sg[x] |= 1;
  return 0;
}
int SG(int x) {
  if (res.count(x)) return res[x];
  int ans = 0, mask = 0;
  set<int> p;
  for (int i = 0; (1 << i) <= x; i++) {
    p.insert(SG(x & ((1 << i) - 1) | (x >> (i + 1))));
  }
  while (p.count(ans)) ++ans;
  res[x] = ans;
  return ans;
}
int main() {
  scanf("%d", &n);
  sg.clear();
  res.clear();
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    Prime(a[i]);
  }
  long long pd = 0;
  for (map<int, int>::iterator it = sg.begin(); it != sg.end(); it++) {
    pd ^= SG(it->second);
  }
  if (pd)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
