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 maxn = 1e5 + 111;
int m = 0, p[200], c[200];
map<int, int> vec, sg;
void divide(int n) {
  m = 0;
  for (int i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      p[++m] = i, c[m] = 0;
      while (n % i == 0) n /= i, c[m]++;
    }
  }
  if (n > 1) p[++m] = n, c[m] = 1;
}
int dfs(int mask) {
  if (!mask) return 0;
  if (sg.find(mask) != sg.end()) return sg[mask];
  int mx = 0;
  for (int i = 1; i < 30; i++)
    if (mask >> i & 1) mx = i;
  int vis = 0;
  for (int i = 1; i <= mx; i++) {
    int tmask = ((mask >> (i + 1)) << 1) | (mask & ((1 << i) - 1));
    vis |= (1 << dfs(tmask));
  }
  int res = 0;
  for (int i = 30; i >= 0; i--)
    if (~vis >> i & 1) res = i;
  return sg[mask] = res;
}
int main() {
  int n;
  scanf("%d", &n);
  while (n--) {
    long long x;
    scanf("%lld", &x);
    divide(x);
    for (int j = 1; j <= m; ++j) {
      vec[p[j]] |= (1 << c[j]);
    }
  }
  int sum = 0;
  for (auto it = vec.begin(); it != vec.end(); it++) sum ^= dfs(it->second);
  printf("%s\n", (sum == 0 ? "Arpa" : "Mojtaba"));
  return 0;
}
