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>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops")
#pragma GCC optimize("no-stack-protector,fast-math")
using namespace std;
const long long N = 1e6 + 1000, OO = 1e15 + 7, T = 13, M = 998244353, P = 6151,
                SQ = 360, lg = 34;
vector<long long> v[N];
unordered_map<long long, long long> mp, mark, it;
long long gra(long long msk) {
  if (it[msk]) {
    return mark[msk];
  }
  bool is[lg] = {};
  for (long long i = 1; (msk >> i) > 0; i++)
    is[gra((msk >> i) | (msk & ((1 << i) - 1)))] = true;
  it[msk] = true;
  for (long long i = 0; i < lg; i++) {
    if (!is[i]) {
      return (mark[msk] = i);
    }
  }
}
int32_t main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  long long n, nxt = 1;
  cin >> n;
  it[0] = true;
  mark[0] = 0;
  for (long long k = 0; k < n; k++) {
    long long x;
    cin >> x;
    for (long long i = 2; i * i <= x; i++) {
      long long k = 0;
      while (x % i == 0) k++, x /= i;
      if (k) {
        if (!mp[i]) mp[i] = nxt++;
        v[mp[i]].push_back(k);
      }
    }
    if (x > 1) {
      if (!mp[x]) mp[x] = nxt++;
      v[mp[x]].push_back(1);
    }
  }
  long long ans = 0;
  for (long long i = 1; i < nxt; i++) {
    long long msk = 0;
    for (auto u : v[i]) msk |= (1ll << u);
    ans ^= gra(msk);
  }
  if (ans == 0)
    cout << "Arpa" << endl;
  else
    cout << "Mojtaba" << endl;
  return 0;
}
