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 N = 1000005;
const double EPS = 1e-9;
const double PI = acos(-1);
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
map<int, long long> p;
map<long long, int> dp;
long long shift(long long mask, int kam) {
  long long ret = 0;
  for (int i = 0; i < kam; i++)
    if (mask & (1ll << i)) ret |= (1ll << i);
  for (int i = kam; i < 30; i++) {
    if (mask & (1ll << i)) ret |= (1ll << (i - kam));
  }
  return ret;
}
int grundy(long long mask) {
  if (dp.count(mask)) return dp[mask];
  set<int> st;
  for (int i = 1; i < 30; i++) {
    if ((1ll << i) <= mask) st.insert(grundy(shift(mask, i)));
  }
  int ret = 0;
  while (st.count(ret)) ret++;
  return dp[mask] = ret;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int a;
    scanf("%d", &a);
    for (int j = 2; j * j <= a; j++) {
      int sum = 0;
      while (a % j == 0) a /= j, sum++;
      if (sum) p[j] |= (1ll << sum);
    }
    if (a > 1) p[a] |= 2ll;
  }
  int sum = 0;
  dp[0] = 0;
  dp[1] = 0;
  for (map<int, long long>::iterator it = p.begin(); it != p.end(); it++) {
    sum ^= grundy(it->second);
  }
  if (sum)
    cout << "Mojtaba";
  else
    cout << "Arpa";
  return 0;
}
