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;
map<int, int> primos;
map<int, int> dp;
int f(int i) {
  if (i <= 1) return i;
  if (dp.count(i)) return dp[i];
  set<int> out;
  for (int j = 0; (1 << j) <= i; j++) {
    int ficanormal = i & ((1 << j) - 1);
    int vaishiftar = (i ^ ficanormal);
    out.insert(f((vaishiftar >> (j + 1)) | ficanormal));
  }
  int ans = 0;
  for (set<int>::iterator it = out.begin(); it != out.end(); it++) {
    if (*it != ans) break;
    ans++;
  }
  return dp[i] = ans;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int a;
    scanf("%d", &a);
    for (int j = 2; j <= sqrt(a); j++) {
      int c = 0;
      while (a % j == 0) {
        a /= j;
        c++;
      }
      if (c) {
        if (!primos.count(j)) primos[j] = 0;
        primos[j] |= (1 << c - 1);
      }
    }
    if (a != 1) primos[a] |= 1;
  }
  int ans = 0;
  for (map<int, int>::iterator it = primos.begin(); it != primos.end(); it++) {
    ans ^= f(it->second);
  }
  printf("%s\n", ans ? "Mojtaba" : "Arpa");
}
