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 maxm = 32000;
int prime[maxm], primeCnt;
void init() {
  static bool isPrime[maxm];
  memset(isPrime, 1, sizeof(isPrime));
  for (int i = 2; i * i < maxm; i++)
    if (isPrime[i])
      for (int j = i * i; j < maxm; j += i) isPrime[j] = 0;
  for (int i = 2; i < maxm; i++)
    if (isPrime[i]) prime[++primeCnt] = i;
}
unordered_map<int, int> mask;
void resolve(int x) {
  for (int i = 1; prime[i] * prime[i] <= x && i <= primeCnt; i++) {
    int t = 0;
    while (x % prime[i] == 0) {
      t++;
      x /= prime[i];
    }
    if (t > 0) mask[prime[i]] |= 1 << t - 1;
  }
  if (x != 1) mask[x] |= 1;
}
unordered_map<int, int> sg;
int getSg(int x) {
  if (x == 0) return 0;
  if (sg.count(x)) return sg[x];
  bool vis[64];
  memset(vis, 0, sizeof(vis));
  for (int i = 0; (1 << i) <= x; i++) {
    int y = (x & ((1 << i) - 1)) | (x >> i + 1);
    vis[getSg(y)] = 1;
  }
  for (int i = 0; i < 64; i++)
    if (!vis[i]) return sg[x] = i;
}
int main() {
  init();
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    resolve(x);
  }
  int ans = 0;
  for (auto &p : mask) ans ^= getSg(p.second);
  if (ans)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
