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;
unordered_map<int, int> prime, dp;
void insert(int num) {
  int hold = 0;
  for (int i = 2; i * i <= num; i++) {
    hold = 0;
    while (num % i == 0) {
      hold++;
      num /= i;
    }
    prime[i] |= (1 << hold);
  }
  if (num > 1) prime[num] |= (1 << 1);
}
int n;
int grundy(int mask) {
  if (dp.count(mask)) return dp[mask];
  int maxk = 0;
  for (int i = 0; i < 32; i++) {
    if ((mask >> i) & 1) maxk = i;
  }
  unordered_map<int, int> aval;
  for (int i = maxk; i >= 0; i--) {
    int newstate = (mask >> i) | (mask & ((1 << i) - 1));
    if (newstate == mask) continue;
    aval[grundy(newstate)] = 1;
  }
  int ans = 0;
  while (aval.count(ans)) ans++;
  return dp[mask] = ans;
}
int main() {
  prime.clear();
  dp.clear();
  scanf("%d", &n);
  int hold;
  for (int i = 0; i < n; i++) {
    scanf("%d", &hold);
    insert(hold);
  }
  int ans = 0;
  for (const auto& it : prime) {
    ans ^= grundy(it.second);
  }
  if (ans)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
  return 0;
}
