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;
void io() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cout.precision(15);
}
const int MAX = 1e5 + 2;
bool pr[MAX];
vector<int> primes;
int A[101];
map<int, int> dp;
int grun(int mask) {
  if (mask == 0) return 0;
  if (dp.find(mask) != dp.end()) return dp[mask];
  int mx = 0;
  for (int i = 1; i <= 30; i++)
    if ((mask >> (i - 1)) & 1) mx = i;
  set<int> s;
  for (int i = 1; i <= mx; i++) {
    int newmask = mask >> i;
    int unaffected = mask & ((1 << (i - 1)) - 1);
    newmask = newmask | unaffected;
    s.insert(grun(newmask));
  }
  int ret = 0;
  while (s.find(ret) != s.end()) ret++;
  return (dp[mask] = ret);
}
int main(int argc, char* argv[]) {
  io();
  for (int i = 2; i < MAX; i++) {
    if (pr[i]) continue;
    primes.push_back(i);
    for (int j = i + i; j < MAX; j += i) {
      pr[j] = 1;
    }
  }
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> A[i];
  }
  int g = 0;
  for (auto p : primes) {
    int msk = 0;
    for (int i = 1; i <= n; i++) {
      int cnt = 0;
      while ((A[i] % p) == 0) {
        cnt++;
        A[i] /= p;
      }
      if (cnt > 0) {
        msk |= (1 << (cnt - 1));
      }
    }
    g ^= grun(msk);
  }
  sort(A + 1, A + n + 1);
  for (int i = 1; i <= n; i++) {
    if (A[i] > 1 && A[i] != A[i - 1]) {
      g ^= 1;
    }
  }
  if (g == 0)
    cout << "Arpa\n";
  else
    cout << "Mojtaba\n";
  return 0;
}
