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;
using llint = long long;
const int N = 110;
int n;
int a[N];
vector<pair<int, int> > prime_div[N];
vector<int> h[N * 20];
vector<int> vp;
map<int, int> sg;
vector<pair<int, int> > get(llint x) {
  vector<pair<int, int> > v;
  for (llint i = 2; i * i <= x; ++i) {
    if (x % i == 0) {
      int c = 0;
      while (x % i == 0) {
        ++c;
        x /= i;
      }
      v.push_back({i, c});
    }
  }
  if (x != 1) v.push_back({x, 1});
  return v;
}
int ha(vector<int> &v) {
  int ret = 0;
  for (int i : v) ret |= 1 << i;
  return ret;
}
int go(int msk) {
  if (msk == 0) return 0;
  if (sg.count(msk)) return sg[msk];
  int mx = 31 - __builtin_clz(msk);
  set<int> st;
  for (int i = 1; i <= mx; ++i) {
    st.insert(go(msk >> i | msk & ((1 << i) - 1)));
  }
  int &ret = sg[msk];
  for (int x = 0;; ++x)
    if (!st.count(x)) {
      ret = x;
      break;
    }
  return ret;
}
void run() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
  }
  for (int i = 1; i <= n; ++i) {
    prime_div[i] = get(a[i]);
    for (auto p : prime_div[i]) {
      vp.push_back(p.first);
    }
  }
  sort(vp.begin(), vp.end());
  vp.erase(unique(vp.begin(), vp.end()), vp.end());
  for (int i = 1; i <= n; ++i) {
    for (auto &p : prime_div[i]) {
      p.first = lower_bound(vp.begin(), vp.end(), p.first) - vp.begin();
      h[p.first].push_back(p.second);
    }
  }
  int ans = 0;
  for (int i = 0; i < N * 20; ++i) {
    if (h[i].empty()) continue;
    sort(h[i].begin(), h[i].end());
    h[i].erase(unique(h[i].begin(), h[i].end()), h[i].end());
    ans ^= go(ha(h[i]));
  }
  puts(ans ? "Mojtaba" : "Arpa");
}
int main() {
  run();
  return 0;
}
