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, x, ans;
unordered_map<int, long long> f;
unordered_map<int, int> g;
int G(int x) {
  if (g[x]) return g[x];
  unordered_set<int> s;
  for (int i = 0; i <= 29; i++) {
    int y = (x >> (i + 1)) | (x & ((1 << i) - 1));
    if (y >= x) break;
    g[y] = G(y);
    s.insert(g[y]);
  }
  int ans = 0;
  while (s.find(ans) != s.end()) ans++;
  g[x] = ans;
  return ans;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x);
    for (int p = 2; p * p <= x; ++p) {
      if (x % p == 0) {
        int cn = 0;
        while (x % p == 0) {
          ++cn;
          x /= p;
        }
        f[p] |= 1 << (cn - 1);
      }
    }
    if (x > 1) f[x] |= 1;
  }
  unordered_map<int, long long>::iterator I;
  for (I = f.begin(); I != f.end(); I++) {
    ans ^= G(I->second);
  }
  puts(ans ? "Mojtaba" : "Arpa");
}
