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 N = 2e5 + 9, M = 1e6 + 9, OO = 0x3f3f3f3f;
const long long llOO = 0x3f3f3f3f3f3f3f3f;
vector<bool> isPrime(N, true);
vector<int> primes;
void sieve() {
  isPrime[0] = isPrime[1] = 0;
  for (int i = 2; i < N; i++) {
    if (isPrime[i]) {
      primes.push_back(i);
      for (int j = i; j < N; j += i) {
        if (j != i) isPrime[j] = false;
      }
    }
  }
}
map<int, int> dp;
int grundy(int mask) {
  if (dp.count(mask)) return dp[mask];
  int &ret = dp[mask] = 0;
  set<int> states;
  int cnt = __builtin_popcount(mask);
  for (int i = 0; cnt; i++) {
    cnt -= (mask >> i) & 1;
    int shifted_mask = (mask >> (i + 1)) | (mask & ((1 << i) - 1));
    states.insert(grundy(shifted_mask));
  }
  int grundy_num = 0;
  while (states.count(grundy_num)) grundy_num++;
  return ret = grundy_num;
}
int main() {
  cin.tie(0);
  cin.sync_with_stdio(0);
  sieve();
  int n;
  cin >> n;
  map<int, int> mask;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    for (auto p : primes) {
      int cnt = 0;
      while (x % p == 0) x /= p, cnt++;
      if (cnt) {
        if (mask.count(p) == 0) mask[p] = 0;
        mask[p] |= (1 << (cnt - 1));
      }
    }
    if (x > 1) mask[x] |= 1;
  }
  int state = 0;
  for (auto p : mask) {
    state ^= grundy(p.second);
  }
  if (state)
    cout << "Mojtaba";
  else
    cout << "Arpa";
}
