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;
unordered_map<int, int> mask, f;
int SG(int s) {
  if (f.count(s)) return f[s];
  bool t[30] = {0};
  for (int i = 0; s >> i; i++) {
    t[SG(s >> (i + 1) | (s & ((1 << i) - 1)))] = 1;
  }
  for (int i = 0; i < 30; i++)
    if (!t[i]) return f[s] = i;
  return 30;
}
int main() {
  scanf("%d", &n);
  for (int i = 1, x; i <= n; i++) {
    scanf("%d", &x);
    for (int d = 2; d * d <= x; d++)
      if (x % d == 0) {
        int c = 0;
        while (x % d == 0) x /= d, c++;
        mask[d] |= 1 << (c - 1);
      }
    if (x > 1) mask[x] |= 1;
  }
  int ans = 0;
  for (auto s : mask) ans ^= SG(s.second);
  puts(ans ? "Mojtaba" : "Arpa");
  return 0;
}
