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 namespace std::chrono;
using hash_t = unsigned long long;
const int MAXN = 123;
const int MAXDEG = 100;
const int MAXREC = MAXDEG * MAXDEG;
int a[MAXN];
int bins[MAXREC][MAXN];
size_t length[MAXREC];
bool was[MAXREC][MAXDEG];
hash_t zob[MAXN][MAXDEG];
vector<pair<int, int> > factors[MAXN];
map<hash_t, int> memo;
int go(int depth) {
  if (length[depth] == 0) return 0;
  hash_t cur_hash = 0;
  for (size_t i = 0; i < length[depth]; i++) cur_hash ^= zob[i][bins[depth][i]];
  if (memo.count(cur_hash)) return memo[cur_hash];
  for (int i = 0; i < MAXDEG; i++) was[depth][i] = false;
  for (int i = 1; i <= bins[depth][length[depth] - 1]; i++) {
    length[depth + 1] = 0;
    for (size_t j = 0; j < length[depth]; j++) {
      if (bins[depth][j] < i)
        bins[depth + 1][length[depth + 1]++] = bins[depth][j];
      else if (bins[depth][j] > i)
        bins[depth + 1][length[depth + 1]++] = bins[depth][j] - i;
    }
    sort(bins[depth + 1], bins[depth + 1] + length[depth + 1]);
    was[depth][go(depth + 1)] = true;
  }
  for (int i = 0; i < MAXDEG; i++)
    if (not was[depth][i]) return memo[cur_hash] = i;
  throw 1;
}
int solve(vector<int> &bins_) {
  sort(bins_.begin(), bins_.end());
  length[0] = bins_.size();
  for (size_t i = 0; i < length[0]; i++) bins[0][i] = bins_[i];
  return go(0);
}
int main() {
  cin.sync_with_stdio(false);
  cin.tie(0);
  mt19937_64 gen;
  gen.seed(12345);
  for (int i = 0; i < MAXN; i++)
    for (int j = 0; j < MAXDEG; j++) zob[i][j] = gen();
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    int cur = a[i];
    for (int j = 2; j * j <= cur; j++) {
      if (cur % j) continue;
      int cnt = 0;
      while (cur % j == 0) {
        cur /= j;
        cnt++;
      }
      factors[i].emplace_back(j, cnt);
    }
    if (cur > 1) factors[i].emplace_back(cur, 1);
  }
  set<int> unique_factors;
  for (int i = 1; i <= n; i++)
    for (auto &u : factors[i]) {
      unique_factors.insert(u.first);
    }
  int answer = 0;
  for (int factor : unique_factors) {
    vector<int> bins_;
    for (int i = 1; i <= n; i++) {
      for (auto &u : factors[i]) {
        if (u.first == factor) bins_.push_back(u.second);
      }
    }
    answer ^= solve(bins_);
  }
  cout << (answer == 0 ? "Arpa" : "Mojtaba") << endl;
  return 0;
}
