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 cnt[100];
int a[110];
int Solve[110];
int dp[110][110][2];
map<int, int> Add;
map<int, int> f;
int grundy(int x) {
  if (f.count(x)) {
    return f[x];
  }
  set<int> can;
  for (int h = 1; h <= 30; ++h) {
    int mask = 0, least = 0;
    for (int i = 1; i <= 30; ++i) {
      if (x & (1 << i)) {
        if (i < h) {
          mask |= 1 << i;
        } else if (i > h) {
          mask |= 1 << (i - h);
        }
      }
    }
    if (mask != x) can.insert(grundy(mask));
  }
  int ans = 0;
  while (can.count(ans)) {
    ++ans;
  }
  return f[x] = ans;
}
int main() {
  if (fopen("1.inp", "r")) {
    freopen("1.inp", "r", stdin);
  }
  int n, tot = 1;
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    if (x != 1) {
      tot = 0;
    }
    int old = x;
    for (int k = 2; k * k <= old; ++k) {
      int val = 0;
      while (x % k == 0) {
        ++val;
        x /= k;
      }
      if (val > 0) Add[k] |= 1 << (val);
    }
    if (x > 1) {
      Add[x] |= 2;
    }
  }
  int ans = 0;
  for (map<int, int>::iterator it = Add.begin(); it != Add.end(); ++it) {
    ans ^= grundy(it->second);
  }
  if (ans) {
    cout << "Mojtaba";
  } else {
    cout << "Arpa";
  }
  return 0;
}
