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, n, a[1010];
map<int, int> b, sg;
void get(int x) {
  int i, nt;
  if (sg.count(x)) return;
  int v[32];
  memset(v, 0, sizeof(v));
  for (i = 1; x >> (i - 1); i++) {
    nt = (x >> i) | (x & ((1 << i - 1) - 1));
    get(nt);
    v[sg[nt]] = 1;
  }
  for (i = 0;; i++)
    if (!v[i]) {
      sg[x] = i;
      return;
    }
}
int main() {
  int i, j, x;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%lld", &a[i]);
  for (i = 1; i <= n; i++) {
    for (j = 2; j * j <= a[i]; j++)
      if (a[i] % j == 0) {
        x = 0;
        while (a[i] % j == 0) a[i] /= j, x++;
        b[j] |= 1 << (x - 1);
      }
    if (a[i] > 1) b[a[i]] |= 1;
  }
  sg[0] = 0;
  for (map<int, int>::iterator it = b.begin(); it != b.end(); it++)
    get(it->second), ans ^= sg[it->second];
  if (ans)
    puts("Mojtaba");
  else
    puts("Arpa");
}
