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 INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fll;
unordered_map<int, int> dp;
int msb(int x) { return __builtin_clz(1) - __builtin_clz(x); }
int solve(int mask) {
  if (mask <= 1) return 0;
  if (dp.count(mask)) return dp[mask];
  int maxi = msb(mask);
  vector<int> mex;
  for (int i = 1; i <= maxi; i++) {
    int at = mask;
    for (int j = i; j <= maxi; j++)
      if (mask & (1 << j)) {
        at ^= (1 << j);
        if (i != j) at |= (1 << (j - i));
      }
    mex.push_back(solve(at));
  }
  sort(mex.begin(), mex.end());
  vector<int>::iterator it = unique(mex.begin(), mex.end());
  mex.resize(distance(mex.begin(), it));
  int g = 0;
  int i = 0;
  for (auto k : mex) {
    if (g == k)
      g++;
    else
      break;
  }
  return dp[mask] = g;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  map<int, vector<int>> mp;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    for (int i = 2; i * i <= a; i++)
      if (a % i == 0) {
        int at = 0;
        while (a % i == 0) a /= i, at++;
        mp[i].push_back(at);
      }
    if (a != 1) mp[a].push_back(1);
  }
  int ans = 0;
  for (auto x : mp) {
    sort(x.second.begin(), x.second.end());
    vector<int>::iterator it = unique(x.second.begin(), x.second.end());
    x.second.resize(distance(x.second.begin(), it));
    int at = 0;
    for (int k : x.second) {
      at += 1 << k;
    }
    ans ^= solve(at);
  }
  if (ans == 0)
    cout << "Arpa" << endl;
  else
    cout << "Mojtaba" << endl;
  exit(0);
}
