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<unsigned int, int> ma;
int dfs(unsigned int state) {
  if (state == 1) return ma[1] = 0;
  if (ma.count(state)) return ma[state];
  bool vis[40];
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= 30; i++) {
    if ((state >> i) == 0) break;
    unsigned int tmp = ((state >> i) | (state & ((1 << i) - 1)));
    vis[dfs(tmp)] = 1;
  }
  for (int i = 0;; i++)
    if (!vis[i]) return ma[state] = i;
}
map<int, int> ma2;
int n, a[111];
unsigned int state;
vector<int> vec[100010];
int main() {
  scanf("%d", &n);
  int ans = 0;
  for (int i = 1; i < (n + 1); i++) {
    scanf("%d", &a[i]);
    int cnt = 0;
    for (int j = 2; j * j <= 1000000000; j++) {
      cnt = 0;
      while (a[i] % j == 0) {
        a[i] /= j;
        cnt++;
      }
      if (cnt) vec[j].push_back(cnt);
    }
    if (a[i] > 1 && ma2.count(a[i]) == 0) ma2[a[i]] = 1;
  }
  for (auto it : ma2) ans ^= 1;
  for (int i = 2; i < 100010; i++) {
    if (vec[i].size() == 0) continue;
    sort(vec[i].begin(), vec[i].end());
    vec[i].erase(unique(vec[i].begin(), vec[i].end()), vec[i].end());
  }
  for (int i = 2; i < 100010; i++) {
    if (vec[i].size() == 0) continue;
    state = 0;
    for (int j = 0; j < (vec[i].size()); j++) state |= (1 << vec[i][j]);
    ans ^= dfs(state);
  }
  if (ans == 0)
    puts("Arpa");
  else
    puts("Mojtaba");
}
