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> mm, f, vis;
int q[1000010], ta, p[33], sp[33];
int dfs(int x) {
  if (vis[x]) return f[x];
  vis[x] = true;
  map<int, int> t0;
  for (register int i = 0; i <= 29; ++i) {
    int x0 = (x & sp[i]);
    if (!x0) break;
    int x1 = (x ^ x0) | (x0 >> (i + 1));
    if (x1 != x) t0[dfs(x1)] = 1;
  }
  int tmp = 0;
  while (t0[tmp]) tmp++;
  return f[x] = tmp;
}
int main() {
  p[0] = 1;
  for (register int i = 1; i <= 29; ++i) p[i] = p[i - 1] * 2;
  for (int i = 29; i >= 0; i--) sp[i] = sp[i + 1] + p[i];
  int n;
  scanf("%d", &n);
  for (register int i = 1; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    for (int j = 2; j * j <= x; j++)
      if (!(x % j)) {
        int cnt = 0;
        while (!(x % j)) cnt++, x /= j;
        int tmp = mm[j];
        if (!tmp) q[++ta] = j;
        mm[j] = tmp | p[cnt - 1];
      }
    if (x != 1) {
      int tmp = mm[x];
      if (!tmp) q[++ta] = x;
      mm[x] = tmp | 1;
    }
  }
  int s = 0;
  vis[0] = true;
  for (register int i = 1; i <= ta; ++i) {
    s ^= dfs(mm[q[i]]);
  }
  if (s)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
  return 0;
}
