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 lnf = 0x3f3f3f3f3f3f3f3f;
const double dnf = 1e18;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double pi = acos(-1.0);
const int hp = 13331;
const int maxn = 100100;
const int maxm = 100100;
const int maxp = 100100;
const int up = 100100;
int prime[maxn], cnt = 0;
bool ha[maxn];
void Prime(void) {
  ha[1] = true;
  for (int i = 2; i < maxn; i++) {
    if (!ha[i]) prime[++cnt] = i;
    for (int j = 1; j <= cnt && i * prime[j] < maxn; j++) {
      ha[i * prime[j]] = true;
      if (i % prime[j] == 0) break;
    }
  }
}
int a[200];
int n;
map<int, int> mp;
void only(int x) {
  for (int i = 1; i <= cnt && prime[i] * prime[i] <= x; i++) {
    if (x % prime[i]) continue;
    int pm = 0;
    while (x % prime[i] == 0) {
      pm++;
      x /= prime[i];
    }
    mp[prime[i]] |= (1 << pm);
  }
  if (x > 1) mp[x] |= (1 << 1);
}
map<int, int> mmp;
int get_sg(int x) {
  if (x == 0 || x == 1) return 0;
  if (mmp.count(x)) return mmp[x];
  bool ha[55];
  memset(ha, 0, sizeof(ha));
  for (int i = 1; i <= 32; i++) {
    if ((x >> i) == 0) break;
    ha[get_sg((x >> i) | (x & ((1 << i) - 1)))] = true;
  }
  for (int i = 0;; i++) {
    if (!ha[i]) return mmp[x] = i;
  }
}
int main(void) {
  Prime();
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    only(a[i]);
  }
  int ans = 0;
  for (auto it = mp.begin(); it != mp.end(); it++) ans ^= get_sg(it->second);
  if (ans)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
  return 0;
}
