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 int MAXP = 31700;
bool isPrime[MAXP];
vector<int> primes;
void getPrimes() {
  primes.clear();
  memset(isPrime, 1, sizeof(isPrime));
  for (int i = 2; i < MAXP; ++i) {
    if (isPrime[i]) primes.push_back(i);
    for (int e : primes) {
      int t = e * i;
      if (t >= MAXP) break;
      isPrime[t] = false;
      if (i % e == 0) break;
    }
  }
}
const int MAXN = 100 + 10;
int N, A[MAXN];
int f[MAXP];
map<int, int> h;
int val[40];
map<int, int> sg;
set<int> mex;
int calSG(int S) {
  if (sg.count(S)) return sg[S];
  set<int> mex;
  for (int i = 0; i < 30 && val[i] <= S; ++i) {
    int T = (S >> (i + 1)) | ((val[i] - 1) & S);
    mex.insert(calSG(T));
  }
  int id = 0;
  for (int s : mex) {
    if (s != id)
      break;
    else
      ++id;
  }
  return sg[S] = id;
}
inline int doOneGame(int S) { return calSG(S); }
bool firstWin() {
  int ans = 0;
  for (int e : primes) {
    if (f[e]) ans ^= doOneGame(f[e]);
  }
  for (const auto& m : h) {
    ans ^= doOneGame(m.second);
  }
  return ans != 0;
}
int main() {
  getPrimes();
  for (int i = 0; i < 30; ++i) val[i] = 1 << i;
  sg[0] = 0;
  scanf("%d", &N);
  for (int i = 1; i <= N; ++i) scanf("%d", A + i);
  for (int i = 1; i <= N; ++i) {
    int a = A[i];
    for (int e : primes) {
      if (a < e) break;
      if (a % e) continue;
      int cnt = 0;
      for (; a % e == 0; a /= e) ++cnt;
      f[e] |= 1 << (cnt - 1);
    }
    if (a > 1) h[a] = 1;
  }
  if (firstWin())
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
  return 0;
}
