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 N = 110, M = 100010;
int primes[M], cnt;
bool st[M];
int a[N];
unordered_map<int, int> state, f;
void init() {
  for (int i = 2; i < M; i++) {
    if (!st[i])
      primes[cnt++] = i;
    else {
      for (int j = 0; primes[j] < M / i; j++) {
        st[primes[j] * i] = 1;
        if (i % primes[j] == 0) break;
      }
    }
  }
}
void get_state(int x) {
  for (int i = 2; i <= x / i; i++)
    if (x % i == 0) {
      int cnt = 0;
      while (x % i == 0) {
        cnt++;
        x /= i;
      }
      state[i] |= (1 << (cnt - 1));
    }
  if (x > 1) state[x] |= 1;
}
int get_sg(int x) {
  if (x == 0) return 0;
  if (f.count(x)) return f[x];
  unordered_set<int> S;
  int t = 0, p = x;
  while (p) {
    t++;
    p >>= 1;
  }
  for (int i = 1; i <= t; i++) {
    S.insert(get_sg((x >> i) | (x & ((1 << i - 1) - 1))));
  }
  for (int i = 0;; i++)
    if (!S.count(i)) return f[x] = i;
}
int main() {
  init();
  int n, res = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    get_state(a[i]);
  }
  for (auto t : state) res ^= get_sg(t.second);
  if (res)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
