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;
template <typename T, typename U>
inline void smin(T &a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, U b) {
  if (a < b) a = b;
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = 1LL * a * a % m)
    if (b & 1) ans = 1LL * ans * a % m;
  return ans;
}
const int maxn = 110;
int a[maxn];
int arr[maxn * maxn];
int cat[maxn * maxn][maxn];
map<set<int>, int> mp;
int top;
int recure(set<int> s) {
  if (s.empty()) return 0;
  if (mp.count(s)) return mp[s];
  int d = *(--s.end());
  int vis[maxn];
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= d; i++) {
    set<int> res;
    for (set<int>::iterator it = s.begin(); it != s.end(); it++) {
      if (*it < i)
        res.insert(*it);
      else if (*it > i)
        res.insert(*it - i);
    }
    vis[recure(res)] = 1;
  }
  int g;
  for (int i = 0; i < maxn; i++)
    if (!vis[i]) {
      g = i;
      break;
    }
  mp[s] = g;
  return g;
}
int main() {
  int n, Num = 0;
  cin >> n;
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < n; i++) {
    long long num = 1ll * a[i];
    for (int j = 2; 1ll * j * j <= num; j++) {
      if (num % j) continue;
      while (num % j == 0) num /= j;
      arr[Num++] = j;
    }
    if (num > 1) {
      arr[Num++] = (int)num;
    }
  }
  sort(arr, arr + Num);
  Num = unique(arr, arr + Num) - arr;
  for (int i = 0; i < n; i++) {
    long long num = 1ll * a[i];
    for (int j = 2; 1ll * j * j <= num; j++) {
      if (num % j) continue;
      int cnt = 0;
      while (num % j == 0) num /= j, cnt++;
      int t = lower_bound(arr, arr + Num, j) - arr;
      cat[t][cnt] = 1;
    }
    if (num > 1) {
      int t = lower_bound(arr, arr + Num, (int)num) - arr;
      cat[t][1] = 1;
    }
  }
  int ok = 0;
  for (int i = 0; i < Num; i++) {
    set<int> res;
    res.clear();
    for (int j = 1; j < maxn; j++) {
      if (cat[i][j]) res.insert(j);
    }
    ok ^= recure(res);
  }
  if (ok)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
