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, a[110];
vector<int> prime;
bool flag[40010];
int cnt[40010][110];
void init(int MX) {
  for (int i = 2; i <= MX; i++) {
    if (!flag[i]) prime.push_back(i);
    for (int j = 0; j < prime.size() && i * prime[j] <= MX; j++) {
      flag[i * prime[j]] = 1;
      if (i % prime[j] == 0) break;
    }
  }
}
int ans = 0;
map<int, int> sg, m;
void dfs(int x) {
  if (sg.count(x)) return;
  bool vis[32];
  memset(vis, 0, sizeof(vis));
  for (int i = 1; x >> (i - 1); i++) {
    int mask = (x >> i) | (x & ((1 << (i - 1)) - 1));
    dfs(mask);
    vis[sg[mask]] = 1;
  }
  for (int i = 0;; i++) {
    if (!vis[i]) {
      sg[x] = i;
      return;
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  init(40000);
  for (int j = 0; j < prime.size(); j++) {
    for (int i = 1; i <= n; i++) {
      while (a[i] % prime[j] == 0) {
        a[i] /= prime[j];
        cnt[j][i]++;
      }
      if (cnt[j][i]) m[j] |= (1 << (cnt[j][i] - 1));
    }
  }
  for (int i = 1; i <= n; i++)
    if (a[i] > 1) m[a[i]] |= 1;
  sg[0] = 0;
  for (map<int, int>::iterator it = m.begin(); it != m.end(); it++) {
    dfs(it->second);
    ans ^= sg[it->second];
  }
  puts(ans ? "Mojtaba" : "Arpa");
  return 0;
}
