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;
const int N = 505;
map<int, int> sg, s;
int n;
void work(int x) {
  int tmp = x;
  for (int i = 2; i * i <= tmp; i++) {
    if (x % i == 0) {
      int m = 0;
      while (x % i == 0) m++, x /= i;
      s[i] |= 1 << (m - 1);
    }
  }
  if (x > 1) s[x] |= 1;
}
int SG(int x) {
  map<int, int> vis;
  if (x == 0) return 0;
  if (sg[x]) return sg[x];
  int res = x, m = 0;
  while (res) m++, res >>= 1;
  for (int i = 1; i <= m; i++) {
    res = x >> i | (x & (1 << (i - 1)) - 1);
    vis[SG(res)] = 1;
  }
  for (int i = 0;; i++) {
    if (!vis[i]) return sg[x] = i;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    work(x);
  }
  int ans = 0;
  for (map<int, int>::iterator it = s.begin(); it != s.end(); it++)
    ans ^= SG((*it).second);
  puts(ans ? "Mojtaba" : "Arpa");
}
