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;
template <typename T>
inline bool chkmin(T &a, const T &b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T>
inline bool chkmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
}
const int MAX_N = 2e4 + 5;
const int INF = 0x7fffffff;
const double eps = 1e-6;
int n;
int a[105];
map<int, int> sg;
set<int> primes;
void solve(int first) {
  if (sg.count(first)) return;
  vector<int> mex(30, 0);
  for (int i = 0; first >> i; i++) {
    int nx = ((first >> (i + 1)) | (first & ((1 << i) - 1)));
    solve(nx);
    mex[sg[nx]] = 1;
  }
  int ret = 0;
  for (; mex[ret]; ret++)
    ;
  sg[first] = ret;
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n;
  for (int i = (0), _end_ = (n); i < _end_; ++i) {
    cin >> a[i];
    int tmp = a[i];
    for (int j = 2; j * j <= tmp; j++) {
      if (tmp % j == 0) {
        primes.insert(j);
        while (tmp % j == 0) tmp /= j;
      }
    }
    if (tmp > 1) primes.insert(tmp);
  }
  sg[0] = 0;
  int ans = 0;
  for (auto p : primes) {
    int state = 0;
    for (int i = (0), _end_ = (n); i < _end_; ++i) {
      int cnt = 0;
      while (a[i] % p == 0) {
        a[i] /= p;
        cnt++;
      }
      if (cnt) state |= (1 << (cnt - 1));
    }
    solve(state);
    ans ^= sg[state];
  }
  if (ans)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
