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 B = 31;
const int N = 107;
int a[N];
bool vis[1000007];
map<int, int> state;
map<int, int> sgn;
int tc = -1;
inline int grrr(int mask) {
  if (mask < 2) return 0;
  auto it = sgn.find(mask);
  if (it != sgn.end()) return it->second;
  vector<int> to_clear;
  for (int i = 1; (1 << i) <= mask; ++i) {
    int small = (mask & ((1 << i) - 1));
    int large = (mask >> i);
    int nmask = (small | large);
    if (nmask == mask) continue;
    int val = grrr(nmask);
    to_clear.push_back(val);
  }
  for (int x : to_clear) vis[x] = true;
  int ret = 0;
  while (vis[ret]) ++ret;
  for (int x : to_clear) vis[x] = false;
  return sgn[mask] = ret;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < n; ++i) {
    int x = a[i];
    for (int k = 2; k * k <= x; ++k) {
      int cnt = 0;
      while (x % k == 0) {
        x /= k;
        ++cnt;
      }
      if (cnt) state[k] |= (1 << cnt);
    }
    if (x > 1) state[x] |= 2;
  }
  int res = 0;
  for (auto &qq : state) {
    res ^= grrr(qq.second);
  }
  cout << (res ? "Mojtaba" : "Arpa") << "\n";
  return 0;
}
