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;
const int N = 1000;
int A[N], B[N];
map<int, int> M;
int dfs(int t) {
  vector<int> nw;
  if (M.count(t)) return M[t];
  for (int j = 0; j <= log2(t); ++j) {
    int x = (t >> (j + 1)) | (t & ((1 << j) - 1));
    nw.push_back(dfs(x));
  }
  for (int i = 0; i < 50; ++i) B[i] = 0;
  for (int i = 0; i < nw.size(); ++i) B[nw[i]] = 1;
  int c = 0;
  while (B[c]) c++;
  return M[t] = c;
}
int ai[N];
int n;
int main() {
  M[0] = 0;
  cin >> n;
  int ans = 0;
  for (int i = 1; i <= n; ++i) cin >> ai[i];
  for (int i = 2; i <= 40000; ++i) {
    int d = 0;
    for (int j = 1; j <= n; ++j) {
      int c = 0;
      while (ai[j] % i == 0) ai[j] /= i, c++;
      if (c) d |= 1 << (c - 1);
    }
    ans ^= dfs(d);
  }
  sort(ai + 1, ai + n + 1);
  for (int i = 1, j = 1; i <= n; i = j) {
    while (ai[i] == ai[j]) j++;
    if (ai[i] != 1) ans ^= 1;
  }
  if (ans == 0)
    cout << "Arpa" << endl;
  else
    cout << "Mojtaba" << endl;
}
