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> m, vis;
void calc(int x) {
  for (int i = 2; i * i <= x; ++i) {
    int cnt = 0;
    while (!(x % i)) x /= i, ++cnt;
    if (cnt) m[i] |= 1 << (cnt - 1);
  }
  if (x > 1) m[x] |= 1;
}
int dfs(int t) {
  if (vis.count(t)) return vis[t];
  int cnt = 0, msk = 0;
  bool temp[40] = {};
  for (int i = 0; (1 << i) <= t; ++i)
    temp[dfs((t & msk) | (t >> (i + 1)))] = 1, msk |= (1 << i);
  while (temp[cnt]) ++cnt;
  return vis[t] = cnt;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = (int)1; i <= (int)n; ++i) {
    int x;
    scanf("%d", &x);
    calc(x);
  }
  long long rt = 0;
  for (auto it : m) rt ^= dfs(it.second);
  puts(rt ? "Mojtaba" : "Arpa");
}
