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 prime[100005];
int isp[100005];
int x = 0;
void init_prime() {
  for (int i = 1; i <= 100000; i++) isp[i] = i;
  for (int i = 2; i <= 100000; i++)
    if (isp[i] == i) {
      prime[x++] = i;
      for (int j = i + i; j <= 100000; j += i) isp[j] = i;
    }
}
int a[102];
unordered_map<long long int, int> state;
int solve(long long int mask) {
  if (state.find(mask) != state.end()) return state[mask];
  if (mask == 0) return 0;
  unordered_set<int> st;
  for (int i = 1; (1LL << i) <= mask; i++) {
    long long int next = ((mask >> (i + 1)) << 1) | (mask & ((1LL << i) - 1));
    st.insert(solve(next));
  }
  for (int i = 0;; i++)
    if (st.find(i) == st.end()) {
      state[mask] = i;
      break;
    }
  return state[mask];
}
int main(void) {
  int n;
  scanf("%d", &n);
  init_prime();
  int i, j;
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  int ans = 0;
  for (i = 0; i < x; i++) {
    int p = prime[i];
    long long int mask = 0;
    for (j = 0; j < n; j++) {
      int c = 0;
      while (a[j] % p == 0) {
        a[j] /= p;
        c++;
      }
      if (c == 0) continue;
      mask |= (1 << c);
    }
    state.clear();
    int g = solve(mask);
    ans ^= g;
  }
  for (i = 0; i < n; i++)
    if (a[i] != 1) {
      for (j = i + 1; j < n; j++)
        if (a[j] % a[i] == 0) a[j] /= a[i];
      ans ^= 1;
    }
  if (ans)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
  return 0;
}
