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;
map<int, int> flg;
map<int, int> dp;
void printVc(vector<int> vc) {
  for (int x : vc) cout << " " << x;
  cout << endl;
}
int getGrundy(int msk) {
  if (msk == 0) return 0;
  if (flg[msk]) return dp[msk];
  set<int> st;
  for (int i = 1; i <= 30; i++) {
    int nmask = 0;
    for (int j = 1; j <= 30; j++) {
      if (msk & (1 << j)) {
        if (j < i)
          nmask |= (1 << j);
        else
          nmask |= (1 << (j - i));
      }
    }
    if (nmask & 1) nmask ^= 1;
    if (msk == nmask) break;
    st.insert(getGrundy(nmask));
  }
  flg[msk] = 1;
  for (int i = 0;; i++)
    if (st.count(i) == 0) return dp[msk] = i;
}
vector<int> primeFactor(int n) {
  vector<int> v;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      v.push_back(i);
      int cnt = 0;
      while (n % i == 0) {
        n /= i;
        cnt++;
      }
      v.push_back(cnt);
    }
  }
  if (n > 1) v.push_back(n), v.push_back(1);
  return v;
}
int main() {
  int n;
  cin >> n;
  map<int, int> mp;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    vector<int> v = primeFactor(a);
    for (int i = 0; i < v.size(); i += 2) {
      mp[v[i]] |= (1 << v[i + 1]);
    }
  }
  int xr = 0;
  for (pair<int, int> p : mp) {
    xr ^= getGrundy(p.second);
  }
  if (xr)
    cout << "Mojtaba" << endl;
  else
    cout << "Arpa" << endl;
  return 0;
}
