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 = 1e5 + 9;
unordered_map<int, set<int> > T;
int n, prime[N], tot;
bool vis[N];
void get_pre() {
  const int lim = 1e5;
  for (int i = 2; i <= lim; ++i) {
    if (!vis[i]) prime[++tot] = i;
    for (int j = 1; j <= tot && prime[j] * i <= lim; ++j) {
      vis[i * prime[j]] = 1;
      if (i % prime[j] == 0) break;
    }
  }
}
struct Hash {
  unsigned long long operator()(const std::set<int> &st) const {
    unsigned long long res = 0;
    for (int i : st) res = res * 37 + i;
    res = res * 41 + st.size();
    return res;
  }
};
std::unordered_map<std::set<int>, int, Hash> dp;
int SG(set<int> st) {
  if (st.empty()) return 0;
  if (dp.count(st)) return dp[st];
  set<int> sg;
  for (int i = *--st.end(); i; --i) {
    set<int> ne;
    for (int j : st) {
      ne.insert(j >= i ? j - i : j);
    }
    if (*ne.begin() == 0) ne.erase(ne.begin());
    sg.insert(SG(ne));
  }
  int res = 0;
  for (; sg.count(res); ++res)
    ;
  return dp[st] = res;
}
int main() {
  scanf("%d", &n);
  get_pre();
  for (int i = 1, x; i <= n; ++i) {
    scanf("%d", &x);
    for (int j = 1; j <= tot; ++j)
      if (x % prime[j] == 0) {
        int tmp = 0;
        while (x % prime[j] == 0) ++tmp, x /= prime[j];
        T[prime[j]].insert(tmp);
      }
    if (x > 1) T[x].insert(1);
  }
  int sg = 0;
  for (auto now : T) {
    sg ^= SG(now.second);
  }
  puts(sg ? "Mojtaba" : "Arpa");
  return 0;
}
