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>
const int kMax = 100007;
std::map<std::vector<int>, int> memory;
bool isPrime[kMax];
int prime[kMax], primeNum;
void GetPrime() {
  memset(isPrime, true, sizeof(isPrime));
  isPrime[0] = isPrime[1] = false;
  for (int i = 2; i < kMax; ++i) {
    if (isPrime[i]) prime[primeNum++] = i;
    for (int j = 0; j < primeNum && (long long)prime[j] * i < kMax; ++j) {
      isPrime[prime[j] * i] = false;
      if (i % prime[j] == 0) break;
    }
  }
}
int factor[2][67], factorNum;
void GetFactor(int n) {
  factorNum = 0;
  for (int i = 0; (long long)prime[i] * prime[i] <= n; ++i) {
    factor[1][factorNum] = 0;
    if (n % prime[i] == 0) {
      factor[0][factorNum] = prime[i];
      while (n % prime[i] == 0) {
        ++factor[1][factorNum];
        n /= prime[i];
      }
      ++factorNum;
    }
  }
  if (n != 1) {
    factor[0][factorNum] = n;
    factor[1][factorNum++] = 1;
  }
}
int SG(const std::vector<int> &vec) {
  auto it = memory.find(vec);
  if (it != memory.end()) return it->second;
  if (vec.empty()) return 0;
  bool sg[2507];
  memset(sg, false, sizeof(sg));
  for (int i = 1; i <= vec[0]; ++i) {
    std::vector<int> next;
    for (int v : vec) {
      if (v > i)
        next.push_back(v - i);
      else if (v < i)
        next.push_back(v);
    }
    std::sort(next.begin(), next.end(), std::greater<int>());
    sg[SG(next)] = true;
  }
  for (int i = 0; i < 2507; ++i)
    if (sg[i] == false) return memory[vec] = i;
  return -1;
}
int main() {
  GetPrime();
  std::unordered_map<int, std::vector<int>> factorMap;
  int N, ans = 0;
  scanf("%d", &N);
  for (int i = 0, a; i < N; ++i) {
    scanf("%d", &a);
    GetFactor(a);
    for (int j = 0; j < factorNum; ++j)
      factorMap[factor[0][j]].push_back(factor[1][j]);
  }
  for (auto &p : factorMap) {
    std::sort(p.second.begin(), p.second.end(), std::greater<int>());
    ans ^= SG(p.second);
  }
  printf("%s\n", ans ? "Mojtaba" : "Arpa");
  return 0;
}
