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;
int ans = 0;
map<int, int> mapa;
unordered_map<int, int> g;
void fat(int n) {
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      int cont = 0;
      while (n % i == 0) n /= i, cont++;
      mapa[i] |= (1 << (cont - 1));
    }
  }
  if (n > 1) {
    mapa[n] |= 1;
  }
}
int grundy(int mask) {
  if (g[mask]) return g[mask];
  if (!mask) return 1;
  int mex = 0;
  int j;
  for (j = 31; j >= 0 && !(mask & (1 << j)); j--)
    ;
  for (int i = 0; i <= j; i++) {
    mex |= 1 << (grundy(mask >> (i + 1) | (mask & ((1 << (i)) - 1))) - 1);
  }
  for (int i = 0; i < 31; i++)
    if (!(mex & (1 << i))) return g[mask] = i + 1;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    fat(x);
  }
  int ans = 0;
  for (auto it = mapa.begin(); it != mapa.end(); it++) {
    ans ^= grundy(it->second) - 1;
  }
  if (ans)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
  return 0;
}
