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 <int n>
using AI = array<int, n>;
const double eps = 1e-9;
const int oo = 0x3F3F3F3F;
const long long ooLL = 0x3F3F3F3F3F3F3F3FLL;
const int MOD = 1000000007;
template <typename T>
T sqr(T x) {
  return x * x;
}
const double PI = acos(-1.);
long long Round(double x) { return x < 0 ? x - .5 : x + .5; }
int main() {
  void run();
  run();
  return 0;
}
int n, a[111];
map<int, int> g;
int gt(int m) {
  if (g.count(m)) return g[m];
  int &rs = g[m];
  rs = 0;
  if (!m) return rs;
  set<int> ng;
  for (int k = 0; (1 << k) <= m; ++k) {
    int np = m >> (k + 1), pp = m & ((1 << k) - 1);
    ng.insert(gt(np | pp));
  }
  while (ng.count(rs)) ++rs;
  return rs;
}
void run() {
  scanf("%d", &n);
  for (int i = (0), _b(n); i < _b; ++i) scanf("%d", a + i);
  map<int, int> ps;
  for (int i = (0), _b(n); i < _b; ++i) {
    for (int j = 2; j * j <= a[i]; ++j) {
      int k = 0;
      while (a[i] % j == 0) a[i] /= j, ++k;
      if (k) ps[j] |= 1 << (k - 1);
    }
    if (a[i] > 1) ps[a[i]] |= 1;
  }
  int rs = 0;
  for (auto &p : ps) rs ^= gt(p.second);
  puts(rs ? "Mojtaba" : "Arpa");
}
