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 maxn = 100 + 10, maxp = 32000;
int a[maxn];
bool v[maxp];
vector<int> prime;
map<int, int> mask, sg;
set<int> has;
void sieve() {
  for (int i = 2; i < maxp; ++i) {
    if (!v[i]) prime.push_back(i);
    for (int j = 0; i * prime[j] < maxp; ++j) {
      v[i * prime[j]] = true;
      if (i % prime[j] == 0) break;
    }
  }
}
int go(int m) {
  if (m == 0) return 0;
  if (sg.count(m)) return sg[m];
  bitset<maxn> v;
  for (int k = 1; k <= 30; ++k)
    if (m >> (k - 1)) {
      int s = go((m >> k) | (m & ((1 << (k - 1)) - 1)));
      if (s < maxn) v[s] = true;
    }
  for (int i = 0; i < maxn; ++i) {
    if (!v[i]) return sg[m] = i;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  sieve();
  int n;
  cin >> n;
  int x = 0;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    int t = a[i];
    for (int j : prime) {
      int c = 0;
      while (t % j == 0) t /= j, ++c;
      if (c) mask[j] |= (1 << (c - 1));
    }
    if (t > 1 && !has.count(t)) x ^= 1, has.insert(t);
  }
  for (int j : prime) x ^= go(mask[j]);
  cout << (x ? "Mojtaba" : "Arpa") << endl;
  return 0;
}
