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 long long INF = 5e18;
const long long MB = 30;
const long long MOD = 1e9 + 7;
map<long long, long long> dp;
vector<pair<long long, long long>> getDivs(long long x) {
  vector<pair<long long, long long>> res;
  for (long long d = 2; d * d <= x; d++) {
    if (x % d == 0) {
      res.push_back({d, 0});
      while (x % d == 0) {
        res.back().second++;
        x /= d;
      }
    }
  }
  if (x > 1) res.push_back({x, 1});
  return res;
}
long long change(long long mask, long long k) {
  return (mask >> k) | (mask & ((1 << k) - 1));
}
long long get(long long mask) {
  if (mask == 1) return 0;
  if (dp.count(mask)) return dp[mask];
  vector<bool> used(MB + 1);
  for (long long k = 1; k < MB; k++) {
    if (change(mask, k) != mask) {
      long long x = get(change(mask, k));
      used[x] = true;
    }
  }
  for (long long i = 0; i <= MB; i++)
    if (!used[i]) return dp[mask] = i;
}
void solve() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  map<long long, long long> mp;
  for (long long i = 0; i < n; i++) {
    vector<pair<long long, long long>> divs = getDivs(a[i]);
    for (auto& p : divs) mp[p.first] = mp[p.first] | (1LL << p.second);
  }
  long long ans = 0;
  for (auto& p : mp) {
    long long mask = p.second | 1;
    ans ^= get(mask);
  }
  cout << (ans ? "Mojtaba" : "Arpa");
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long t = 1;
  while (t--) solve();
}
